ct 2m

CIRCUIT THEORYEC T35UNIT-1PART-A (2 MARKS) 1. State Tellegens theoremTellegen's theorem is one of the most powerful theorems in network theory. Most of the energy distribution theorems and extreme principles in network theory can be derived from it. Tellegen's theorem gives a simple relation between magnitudes that satisfy Kirchhoff's laws of electrical circuit theory.

2. State maximum power transfer theoremMaximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals.

3. Define thevenins theorem Thevenins theorem is a theorem in electrical circuit theory that allows any one-port network to be reduced to a single generator and single impedance. It was originally stated in terms of DC resistive circuits only.

4. State difference between thevenins and Nortons theorem Nortons theorem uses a current source, whereas Thevenins theorem uses a voltage source. Thevenins theorem uses a resistor in series, while Nortons theorem uses a resister set in parallel with the source. Nortons theorem is actually a derivation of the Thevenins theorem.

5. Limitations of Thevenins theoremA limitation of Thevenins theorem is that, it assumes that the circuit is completely linear. So, this theorem is applicable for resistors, but will not work well when trying to analyze circuits consisting of non-linear elements such as diodes.

6. What are active and passive elements?Circuit analysis is the process by which voltage or current is measured across the element. In a complete circuit there are two types of elements found active elements and passive elements. The active elements generate energy. Batteries, generators, operational amplifiers etc are active elements. The passive elements cannot generate energy, they drop energy. Resistor, capacitor, inductor etc are passive elements because they take energy from circuit.

7. What is linear network?A network in which the parameters of resistance, inductance, and capacitance are constant with respect to current or voltage, and in which the voltage or current of sources is independent of or directly proportional to other voltages and currents, or their derivatives, in the network therefore it is known as linear network.

8. What is active network?Elements which supply the energy to the circuit are known as active elements. Anetwork which contains active elements is known as active networks.Ex: batteries, generators, transistors etc.

9. Define non linear network.Most electronic designs are, in reality, non-linear. There is very little that does not include some semiconductor devices. These are invariably non-linear; the transfer function of an ideal semiconductor pn junction is given by the very non-linear relationship;

10. What is bilateral network?A bilateral network element can conduct current equally well in either directions. That means, it will have, same voltage current flow.

11. Define unilateral network.In unilateral circuits, the property of circuit changes with the change of direction of supply voltage or current. In other words, unilateral circuit allows the current to flow only in one direction. Diode rectifier is the best example of unilateral circuit because it does not perform the rectification in both direction of supply.

12. State ohms law.Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

13. What is compensation theorem?This theorem is based on one basic concept. According to Ohm's law, when current flows through any resistor, there would be a voltage drop across the resistor. This dropped voltage opposes the source voltage. Hence voltage drop across a resistance in any network can be assumed as a voltage source acting opposite to the source voltage. Then it is called as compensation theorem.

14. State Millmans theorem?In Millman's Theorem, the circuit is re-drawn as a parallel network of branches, each branch containing a resistor or series battery/resistor combination. Millman's Theorem is applicable only to those circuits which can be re-drawn accordingly.

15. What is superposition theorem? It states that in an active, linear, bilateral network consisting of active and passiveelements with more than one source, the overall response (voltage or current) is equalto the sum of the responses due to each of the sources acting independently.16. Mention the disadvantages of Ohms Law.

It does not apply to all non metallic conductorsIt also does not apply to non linear devices such as zener diode, vacuum tubes etc.It is true for metal conductors at constant temperature. If the temperature changes the law is not applicable.17.What are the classifications of Circuit elements?

Active element

Passive element

Lumped and distributed elements

Bilateral and unilateral elementsLinear and non linear elements.18. State the steps to solve the Thevenins theorem.

Remove the load resistance and find the open circuit voltage VOC

Deactivate the consta t sources (fro voltage source remove it by internal resistance & for current source delete the source by OC) and find the internal resistance (RTH) of the source side looking through the open circuited load terminals

Obtain the Thevenins equivalent circuit by connecting VOC in series with RTH

Reconnect the load resistance across the load terminals.19.State the steps to solve the Nortons theorem.

Remove the load resistor and find the internal resistance of the source N/W by deactivating the constant source.

Short the load terminals and find the short circuit current

Nortons equivalent circuit is drawn by keeping R TH in parallel with ISC.20.Write some applications of maximum power transfer theorem.

Power amplifiers

Communication system

Microwave transmission

21. What is the limitation of superposition theorem?

This theorem is valid only for linear systems. This theorem can be applied for calculating the current through or voltage across in particular element. But this superposition theorem is not applicable for calculation of the power.

22.What are the limitations of maximum power transfer theorem?

The maximum efficiency can be obtained by using this theorem is only 50% . It is because of 50% of the power is unnecessarily wasted in Rth.

Therefore this theorem only applicable for communication circuits and not for power circuits where efficiency is greater importance rather than power delivered.23. List the applications of Thevinins theorem.

It is applied to all linear circuits including electronic circuits represented by the controlled source.

This theorem is useful when t is desired to know the effect of the response in network or varying part of the network.24.State voltgae division rule.

Voltage across a resistor in a series ciruict is equal to the total voltage across elements mulitiplied by the value of that resistor divided by the total resistance of the series elements.V1=(R1)*V/ (R1+R2)25.State current division rule.

Current in any branch is equal to the ratio of the opposite parallel branch resistance to the total resistance value, multiplied by the total current in the circuit.

I1=(R2)*I/(R1+R2)26. What is a closed path?

A closed path which starts at a node and travels through some part of the circuit and arrives at the same node without crossing the node or more than once.27. What is a node?

A node is a point in a network in which two or more elements have a common connection.28.What are dependent and independent sources?

The electrical energy supplied by dependent sources a source of electrical energy.

The electrical energy supplied by independent source does not depend on another electrical source. They convert some energy in to electrical form.29. Define series connection.

If the resistances are connected end to end the combination is said to be series.30. Define KCL KCL states that the algebraic sum of currents in node is zero. 31. Define KVL KVL states that the algebraic sum of voltages in a closed path is zero.32. Define lumped network.Any network which can be physically separated are called as lumped network.33. Define distributed network.Any network which cannot be physically separated are called as distributed network.34.What do you mean by an electric network and an electric circuit.Interconnection of two or more simple circuit elements (voltage sources,resistors,inductors and capacitors) is called an electric network. If a network contains at least one closed path, it is called an electric circuit.35.Define electric current.Electric current is defined as rate of flow of electric charge. The unit of current is ampere which is the current that flow when I coulomb of charge is transferred in one second. 36.Define electrical potential or voltage.Voltage is generally measured between two points and its unit is the volt. If the work done in moving a charge of one coulomb between any two points is 1 joule, then we say that the potential of one point with reference to the second point is 1 volt.37.What is meant by resistance?The resistance of the circuit is the property by which it opposes the flow of current. This parameter measured in ohms is responsible for energy dissipation.38. Define conductance.The reciprocal of resistance is called conductance. Its unit is Siemen and its symbol is G.39. What is meant by electric energy?Energy is the total amount of work done and hence is the product of power and time.40. Under what conditions superposition theorems can be applied?Superposition theorems can be applied only when the cause and effect have a linear relationship.41. What is the condition for maximum power transfer?The power delivered is maximum if the load resistance is equal to the source resistance.42. What are the types of circuit elements?Active elements:Voltage and current sourcePassive elements:Resistor, inductor, capacitor.43. What are the types of dependent sources?Voltage dependent voltage source Current dependent voltage source Voltage dependent current source Current dependent current source

44. What are dependent sources?A dependent voltage or current source is one which depends on some other quantity in the circuit which may be either a voltage or a current. Such a source is represented by a diamond shaped symbol.45. Define ideal voltage source.For ideal voltage source, source impedance is zero, such voltage source gives a constant voltage V irrespective of current drawn from it.46. Define ideal current source.For ideal current source, source impedance is infinite , such an ideal current source gives a constant current irrespective of voltage across it47 What are the ideal sources of electrical energy?Ideal voltage sourceIdeal current source.48. A resistor with a current of 3A through it converts 500J of electrical energy to heat energy in 12 sec. What is the voltage across the resistor?Energy=EIt500=E*3*12E=13.88 V.49. A 5ohm resistor has a voltage rating of 100V,what is its power rating?Power=Power=2000W.50.An electric heater draws 8A from 250V supply. What is its power rating? Also find the resistance of the heater element.Power rating= V.I=8*250=2000Watts.Resistance=250\8=31.25ohm.

PART-B (11 MARKS)1. Determine the voltage across the terminal AB in the circuit. Shown in the figure.(11)

10V5AB

6v

5A

2. Determine the maximum power delivered to the load in the circuit.(11)

3. (a) Determine Norton equivalent circuit at terminals AB for the circuit shown below.(6)

(b) Verify the reciprocity theorem in the circuit shown in figure.(5)

4. (a) Find the current through 3 resistance using superposition theorem(6)

(b) Explain Millmans theorem and tellegens theorem(5)5. (a) Find the current in 10 ohm resistor in the circuit using super position theorem(6)(b) State and explain super position theorem(5)

6. (a) State and explain the maximum power transfer theorem (6)(b) Find I in the circuit and verify reciprocity theorem.(5)

7. Find the current in 2 Ohm using super position theorem (11)

8. Calculate the I through 6 Ohm resistor and voltage across 6 ohm resistor using Norton theorem(11)

9. Determine the thevenins equivalent circuit(11)

10. Obtain the Nortons equivalent circuit for the following network (11)

11. (a) Explain series RC circuit with circuit diagram(5)

(b) Find the maximum power transferred the load ZL(6)

100-0V50-90v

12. (a) Determine the thevenins equivalent circuit between the output terminals AB (8)

50-0(b) State K(3)

13. State and explain Kirchoffs law(11)14. Find the power loss in 1 ohm resistor RL using Nortons theorem in fig. shown(11) 15. Use Thevenins theorem to determine the current I flowing in the 4ohm resistor shown in the figure. Find also the power dissipated in the 4ohm resistor.(11)

16. The circuit diagram shows dry cells of source e.m.f 6v, and internal resistance of 2.4ohm. If the load resistance RL is varied from 0 ohm to 5 ohm in 0.5 steps, calculate the power dissipated by the load in each case. Plot a graph RL horizontally against power verticallyand determine the maximum power dissipated. (11)

UNIT-2PART-A (2 MARKS)1. Write the statement for Maximum power transfer theorem.Maximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals.

2. State Norton theorem?Norton's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single current source and parallel resistance connected to a load, similar to thevenins theorem.

3. State Maximum power transfer theoremMaximum power transfer theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must equal the resistance of the source as viewed from its output terminals.

4. What are the types of power used in AC circuitsThe three different types of power in AC circuits are as follows: S = apparent power, measured in Volt-Amps (VA) P = true power, measured in Watts (W)

Q = reactive power, measured in Volt-Amps reactive (VAR)

5. Write some application of maximum power transfer theorem. It is used where maximum power is required It gives throughput Less power reduction

6. What is meant by selectivityResonant circuits are used to respond selectively to signals of a given frequency while discriminating against signals of different frequencies. If the response of the circuit is more narrowly peaked around the chosen frequency, we say that the circuit has higher "selectivity".

7. 10What is anti-resonance circuit?It is a circuit which uses in the amplitude of one oscillator at a particular frequency, accompanied by a large shift in its oscillation phase. Such frequencies are known as the system's anti resonant frequencies, and at these frequencies the oscillation amplitude can drop to almost zero. Anti resonances are caused by destructive interference, for example between an external driving force and interaction with another oscillator.

8. State parallel resonanceThe difference this time however, is that a parallel resonance circuit is influenced by the currents flowing through each parallel branch within the parallel LC tank circuit. A tank circuit is a parallel combination of L and C that is used in filter networks to either select or reject AC frequencies.

9. What are the characteristics of parallel resonanceThe voltage is the same across the inductor and capacitor. The currents through the components vary inversely with their reactance in accordance with Ohm's law. The total current drawn by the circuit is the vector sum of the two individual component currents.

10. Define resonanceResonance in AC circuits implies a special frequency determined by the values of the resistance , capacitance , and inductance .

11. Define quality factor Q of a coil.The quality factor is defined as the ratio of maximum energy stored to the energy dissipated in one period.

12. What is resonant frequency and Q factorA resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism, and even throughout the realm of modern physics.

13. Draw the voltage phasor diagram for both series RL and series RC circuit with needed circuit diagram

14. Define BandwidthThe bandwidth is measured between the 3dB-points, that is, the frequencies at which the power passed through the circuit has fallen to half the value passed at resonance. There are two of these half-power frequencies, one above, and one below the resonance frequency

15. Define series resonanceFor series resonance the condition of resonance is straightforward and it is characterized by minimum impedance and zero phases.16.What are half power frequencies?

In RLC circuits the frequ ncies at which the power is half the max/min power are called half power frequencies.17. Write the characteristics of series resonance.

At resonance impedance in min and equal to resistance therefore current is max.

Before resonant frequency the circuit behaves as capacitive circuit and above resonant frequency the circuit will behave as inductive circuit.

At resonance the magnitude of voltage across the inductance and capacitance will be Q times the supply voltage but they are in phase opposition.18. State the properties of a series RLC circuit.

The applied voltage and the resulting current are in phase, when also means than the p.f of RLC circuit is unity.

The net reactance is zero at resonance and the impedance does not have the resistive part only.

The current in the circuit is max: and is V/R amperes

At resonance the circuit has got minimum impedance and max: curre nt

Frequency of resonance is given by fr=1/(2LC).19.State the properties of a parallel RLC circuit.

PF is unity

Current at resonance is (V/(L/RC)) and is in phase with the applied voltage. The value of current at resonance is minimum.

Net impedance at resonance is max: & is equal to L/RC

The admittance is min: and the net susceptance is zero at resonance.

20. Define mesh.

A mesh is defined as a lo op which does not contain any other loops within it.

21. What is a planar circuit?

A circuit is said to be non planar if it cannot be drawn on a plane surface without crossovers.

22. Define super mesh.

The loop existing around a current source which is common to the two loops is called super mesh.23. Write the general form of mesh and nodal analysis. For mesh, [R][I]= [V]For nodal, [G] [V]=[I]

PART-B (11 MARKS)1. Determine the thevenins equivalent circuit between the output terminals AB. (11)

2. A voltage V(t)=10 sin t in applied to a series RLC circuit at the resonant frequency of the circuit, the maximum voltage across the capacitor is found to be 500 v. moreover, the BW in 400 Rad/sec and the impedance at resonance in 100. Find the resonant frequency. Also find the values of L and C of the circuit. (11)3. (a) derive the bandwidth and Q-factor of parallel resonance with needed diagram (6)(b) Write the mesh current in the circuit shown in figure (5)

4. (a)Find the maximum power transferred to the load ZL (6)

(b) Explain series RC circuit with circuit diagram (5)5. Find ix in the circuit of figure by nodal analysis (11)

6. Find the voltage across (2+j5) Ohm in figure using super position theorem (11)

7. A coil of inductance 318.3 m H and negligible resistance is connected in series with a 200 Ohm resistor to a 240V, 50 Hz supply. Calculate (a) the inductive reactance of the coil, (b) the impedance of the circuit, (c) the current in the circuit, (d) the p.d across each component, and (e) the circuit phase angle.(11)

8. The coil consists of a resistance of 100 Ohm and an inductance of 200mH. If an alternating voltage. V is given by V=200 sin 500t volts is applied across the coil, calculate (a) the circuit impedance, (b) the current flowing, (c) the p.d across the resistance, (d) the p.d. across the inductance and (e) the phase angle between voltage and current.(11)

9. Write a brief notes on series resonance with needed diagram. Derive its resonant frequency, bandwidth and quality factor.(11)

10. Derive the expression bandwidth, resonant frequency and half power frequency for series resonance. (11)

11. Determine the voltage across (2+j5) ohm impedance as shown in figure by using super position theorem. (11)

UNIT-3PART-A (2 MARKS)1. What is transient?A transient event is a short-lived burst of energy in a system caused by a sudden change of state. The source of the transient energy may be an internal event or a nearby event. The energy then couples to other parts of the system, typically appearing as a short burst of oscillation.

2. Sketch the transient response of RL and RC circuits

3. State the difference between natural and forced responseThe difference between the natural response and the forced response of a system is that, although the natural response of a system always decays to zero, the forced response has no such restriction. In fact, the forced response of the system will take the same form as the forcing function, as time goes to infinity.

4. State initial value theoremIn mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches zero. Let

be the (one-sided) Laplace transform of (t). The initial value theorem then says

5. What is final value theorem?In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain behavior as time approaches infinity. A final value theorem allows the time domain behavior to be directly calculated by taking a limit of a frequency domain expression.

6. What is meant by forced response?The behavior of a circuit due to an external energy source, dependent on the form of forcing function. The impedance concept was developed for use in determining natural response; it turns out to be applicable to forced response as well.

7. What is meant by natural response?A transient response or natural response is the response of a system to a change from equilibrium. The transient response is not necessarily tied to "on/off" events but to any event that affects the equilibrium of the system.

8. Write down the time constant of series RL and RC circuitsT = RC and T = L / RThese are the time constant series for RL and RC circuits.

9. Write the characteristics equation of a series RLC circuit when sinusoidal input is given to R.

The characteristic equation for series RLC circuit is given below,

10. Define steady state responseSteady state is an equilibrium condition of a circuit or network that occurs as the effects of transients are no longer important. Steady state determination is an important topic, because many design specifications of electronic systems are given in terms of the steady-state characteristics

11. What is sinusoidal excitationSinusoidal excitation is nothing but the source with the AC as input signal. Hence this is called as sinusoidal excitation.

12. Define transient analysisIt is defined as; it is the response of a system with respect to the input as a function of time

13. What is non sinusoidal excitationIt is nothing but the external source will be non sinusoidal which means DC signal. Therefore non sinusoidal is referred as NON AC input circuit.

14. Define conductanceConductance is defined as the reciprocal of resistance. Therefore it is denoted as Resistance-1

15. Define trans-conductanceTransconductance is the property of certain electronic components. Conductance is the reciprocal of resistance; transconductance is the ratio of the current variation at the output to the voltage variation at the input. It is written as gm.16.What is transient time?

The time taken for the circuit to change from one steady state to another steady state is called transient time.

17. What is transient response?

The storage elements deliver their energy to the resistances, hence the response changes with time, get sturated after sometime, and are referred to the transient response.18. Define time constant of RLC circuit.

The time taken to reach 63.2% of final value in a RL circuit is called the time constant of RL circuit.

Time constant=L/R19.Define time constant of RC circuit.

The time to taken to reach 36.8% of initial current in an RC circuit is called the time constant of RC circuit.

Time constant=RC20.What is meant by natural frequency?

If the damping is made zero then the response oscillates with natural frequency without any opposition, such a frequency is called natural frequency of oscillations.

21. Define damping ratio.

It is the ratio of actual resistance in the circuit to the critical resistance.22.Write down the condition, for the response of RLC series circuit to be under damped for step input.

The condition for the reponse of RLC series circuit to be under damped step input is

(R/2L)2>(1/LC)

23. Write down the condition fo the response of RLC sereis circuit to be over damped for step input.

The condition for the response of RLC series circuit to be over damped for step input is,

(R/2L)2>(1/LC)

24. Write down the few applications of RL, RC, RLC circuits.

Coupling circuits

Phase shift circuits

Filters

Resonant circuits

AC bridge circuits

Transformers25. Define apparent power.

The apparent power is defined as the product of magnitude of voltage and magnitude of current.

PART-B (11 MARKS)1. A series RC circuit consists of resistor of 100 and a capacitor of 0.1F through switch. A constant voltage of 20V is applied to the circuit at t=0. Obtain the current equation. Determine the voltage across the resistor and capacitor.(11)

2. The series RL circuit consists R=150 and L=0.5H. The switch in closed when =30. Determine the resultant current when voltage V=50 cos (100t+ ) in applied to the circuit at = =30. (11)3. Derive the expression for sinusoidal response of RLC circuit (11)4. A series RL circuit with R=30 Ohm and L = 15 H. has a constant voltage V=60 V at t=0. Determine the current I, the voltage across the resistor and the voltage across the inductor. (11)5. (a) derive the expression for RLC series transients to DC excitation (6)(b) Determine the complete solution for the current in a RL circuit (5)

6. The 20 F capacitor has an initial charge Q0=0.001 coulombs. The switch is closed at t=0. Find the transient current. (11)7. Explain the RC transient response of a DC circuit. (11)8. Explain the RLC transient of a DC circuit. (11)9. A 30F capacitor is connected in parallel with an 80 resistor across a 240 V, 50 Hz supply. Calculate (a) a current I each branch (b) the supply current (c) the circuit phase angle (d) the circuit impedance (e) the power dissipated and (f) the apparent power (11)10. Derive the expression dc responses of an RC circuit. Also find power in each element (11) 11. A circuit consists of 20 Ohm resistance, 0.05H inductance, and 20 F capacitance in series and connected to a 100 V constant source through a switch. If the switch is closed t-0. Find the current transient (11)12. A series RC consists of resistor 10 Ohm and capacitor of 0.1F through switch. A transient voltage of 20 V is applied to the circuit t=0. Obtain the current equation and determine the voltage across the resistance and capacitance. (11)13. A series RL circuit consists R=150Ohm and L=1.5H. The switch is closed when =30.determine the resultant current when voltage V=50. Is applied to the circuit when =30. (11)14. A series RLC transient circuit with a constant 100 V source. Find the transient response when switch is closed at t=0 (R=200Ohm, L=0.05H and C=20F) (11)15. Derive the expression for series RC transient with input of V cos (t+) (11)

UNIT-4PART-A (2 MARKS)1. Define tuned circuits.An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, consists of an inductor, denoted by the L, and a capacitor, denoted by the C.

2. Define single tuned circuits.A circuit in which secondary coil alone is tuned or the circuit has one inductor and capacitor connected in such a way that it produces the resonance condition for only one frequency.

3. Define double tuned circuitsA circuit that contains double tuned circuit it has more number of reactive elements and it has two tuning frequency.

4. What are the applications of double tuned circuits?Double tuned amplifiers are used for amplifying radio-frequency (RF) signals. One such application is, it is widely used in the radio receiver circuits.

5. State dot rule for coupled coils If both current enter dotted ends of coupled coils or if both currents leave dotted ends, then the signs on the M-terms will be same as the signs on the L-terms. If one current enters a dotted end and the other an undotted end, the signs on the M-terms will be opposite to the signs on the L-terms.

6. Give a short note on dot ruleWhen the voltage induced by self and mutual inductance (L and M respectively) occur simultaneously, the relative polarities of these two voltages must be determined before making any circuit calculation. The voltage induced in a coil by M may either aid or oppose the voltage of L, depending upon the sense of the windings and the directions of ht currents in the coils. It means that M di2/dt in coil 1 may either be positive or negative with respect to the drop L1 di1/dt in coil . The condition is taken into account by assigning sign to M.

7. What is self inductanceIn a circuit there is flow of I in which the current changes. So, the flux linking with the circuit also changes. According to faradays law of induction, an e.m.f is induced in the circuit. This e.m.f is equal to rate of change of flux linkage.

8. What is meant by double tuned circuit?It is defined as a circuit that contains double tuned circuit it has more number of reactive elements and it has two tuning frequency. A pair of L and C in a single circuit is called as double tuned circuit.

9. Distinguish self and mutual inductanceThe changing electric current flows by the coil, an flux by an coil due to an magnetic flux generate by electric current in them will continue altering. Thus the induced electromotive force. Thus flux by the different coil will continue altering with period; thus an electromotive force.

10. State coefficient of couplingThe coefficient of coupling of a transformer is dependent on the portion of the total flux lines that cuts both primary and secondary windings. Coefficient of coupling k, given by k = M/L1L2

11. What is mutual inductance?When two inductors (or coils) are in a close proximity to each other, the magnetic flux caused by current in one coil links with the other coil, thereby inducing voltage in the latter. This phenomenon is known as mutual inductance

12. What is self inductance?The self inductance of a coil is defined as flux linkage in that coil per 1 ampere current in the same coil. It is also defined as the Weber turns per ampere current in the coil. L is measured in Henry.

13. What is coupled coilsCoupled coils are nothing but there are two coils or pair of coils which may connect via coupled. Therefore these coils are represented as coupled coils.

14. Define multi windingsEach and every transformer will have certain windings. If the transformer has n no. of windings then it is denoted as multi windings.

15. What is series and parallel connection of coupled inductorsInductors are said to be connected together in Parallel when both of their terminals are respectively connected to each terminal of the other inductor Inductors can be connected in a series connection, a parallel connection or combinations of both series and parallel together, to produce more complex networks whose overall inductance is a combination of the individual inductors.16. What is DOT convention?

The sign of mutual induced emf depends on the winding sense and the current through the coil. The winding sense is decided by the manufacturer and to inform the user about the winding sense a dot is placed at one end of each coil. When current enter at dotted end in one coil then the mutual induced emf in the other coil is positive at dot end.

PART-B (11 MARKS)1. Find the ratio of output voltage to input voltage.(11)

Vout2. Find the voltage across the 10 resistor for the given circuit.(11)

3. (a) write a short notes on multi winding coupled circuits and make an analysis with an example of inductively coupled three coils(5)4. (b) Draw the circuit diagram of single tuned coupled circuit and find its mutual inductance(6)5. Calculate the effective inductance of the circuit shown in figure(11)

Vi

6. What is meant by inductively coupled circuits? Explain(11)7. Explain in detail about single tuned and double tuned circuits(11)8. Explain in detail about the double tuned circuits(11)9. Explain the series and parallel connection of coupled inductors in detail(11)10. The resonant frequencies of the tuned circuit shown in figure is 1000r/s. calculate the self inductance of the 2 coils and the optimum value of mutual inductance(11)

11. (a) Difference between self inductance and mutual inductance (2)(b) Find the ratio of output voltage to input voltage (9)12. Define mutual impedance. Explain the property of inductance of a coil (11)13. Explain the terms: self inductance, Mutual inductance and coefficient of coupling (11)14. Derive from first principles an expression for the mutual inductance in terms of the self inductances and the coefficient of coupling.(11)15. (a) Explain the dot conversion used in coupled coils (5)(b) Two mutually coupled coils have self inductance of 50mH and a coupling coefficient of 0.8. If the coils carry currents of 0.5A and 1.5 A respectively, Calculate the two possible vales for energy stored in the magnetic field. (6)

UNIT-5PART-A (2 MARKS)1. What are cut setsCut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset of the partition. These edges are said to cross the cut. In a connected graph, each cut-set determines a unique cut, and in some cases cuts are identified with their cut-sets rather than with their vertex partitions.

2. What is a dual? Give some examples.Dual of a relationship is formed by interchanging voltage and current in an expression. The dual expression thus produced is of the same form, and the reason that the dual is always a valid statement can be traced to the duality of electricity and magnetism.

3. Define connected graph?It is defined as a graph which is connected in the sense of a topological space, i.e., there is a path from any point to any other point in the graph. A graph that is not connected is said to be disconnected. This definition means that the null graph and singleton graph are considered connected, while empty graphs on nodes are disconnected.

4. Write a short note on graph and treeA tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without simple cycles is a tree.

5. What is a tree? Give example.A tree is an undirected simple graph G that satisfies any of the following equivalent conditions: G is connected and has no cycles. G has no cycles, and a simple cycle is formed if any edge is added to G. G is connected, but is not connected if any single edge is removed from G. G is connected and the 3-vertex complete graph is not a minor of G. Any two vertices in G can be connected by a unique simple path.

6. Difference between planar graph & non-planar graph.A planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.Non planar graph has many nodes esp. each and every node will be connected with all the nodes.

7. List out the difference between directed graph and undirected graph.In graph theory an undirected graph G has two kinds of incidence matrices: un-oriented and oriented. The incidence matrix (or un-oriented incidence matrix) of G is a n m matrix , where n and m are the numbers of vertices and edges respectively, such that if the vertex and edge are incident and 0 otherwise.

8. Define degree of the node and tie set.It is defined as a degree or height of node and tie set in other words, the measure of peak value of node and tie set values in order to draw the graph and tree.

9. Define Graph, tree and tie set.Graph is defined as it is made up of "vertices" or "nodes" and lines called edges that connect them.Tree is nothing but collection of nodes and graph. Where tie set is denoted as combination of both graph and tree is said to be tie set.

10. Write the concept of incidence matrix.An incidence matrix is a matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y

11. Difference between branch and linkA main source node has many branches the connectivity for this each node will be equipped with the link. These are the difference between branches and link.

12. What are the advantages of reduced incidence matrix?Let G be a connected digraph with n nodes and b branches. Let Aa be the Incidence Matrix of G. The (n-1) x b matrix an obtained by deleting any one row of Aa is called a Reduced-Incidence Matrix of G.

13. List out the properties of tree and co-tree. Can easily find the error Easy manipulation Contains more logical phenomenon.

14. Define chord.It is a sequence where used to link the two graph. Sometimes it may be called as bridges of two networks.

15. What is known as isomorphism?An isomorphism or equal is a homomorphism (or more generally a morphism) that admits an inverse. Two mathematical objects are isomorphic if an isomorphism exists between them. An automorphism is an isomorphism whose source and target coincide. Hence it is called as isomorphism.

PART-B (11 MARKS)1. Write the incidence matrix, tie set matrix end link control transformation equation for the given topological graph.(11)

2. Obtain the fundamental cut set & free branch voltage equation for the given branch. (11)

3. (a) Define duals. Write the steps followed to draw the duals of any network(5)(b) Draw the dual for the given circuit(6)

4. Explain tree branch voltages and cut set schedules with an example(11)5. Explain the properties of tie-set and cut set(11)6. (a) Explain the incidence and reduced incidence matrix.(6)(b) Define graph, tree and dual networks.(5)7. (a) What is oriented graph? Give example(4)(b) For the network, draw the graph, tree, tie set schedule and find the loop currents and branch voltages.(7)

8. Find the cut set matrix & the branch voltages &currents for the network (11)

9. (a) Explain the concept of incidence matrix(5)

(b) Draw the oriented graph from complete incidence matrix given(6)NodesBranches

abcdef

L-1001-10

M1-1000-1

N01-1010

O001-101

10. (a) For the given graph shown in figure drawn the no. of possible trees.(7)

(b) Write the properties of incidence matrix with an example(4)

11. For the given network,(11)(a) Draw the oriented graph(b) Write the fundamental loop matrix(c) Develop the network equilibrium equations

12. For the circuit shown, (a) draw the oriented graph, (b) select a tree (c) draw tie set schedule (11)

13. For the network shown write the fundamental cut set matrix and hence obtain the equations on basis of node analysis. The conductance are expressed in Siemens (11)

14. Draw the graph for the network shown in figure and draw all the possible trees (11)

15. Write down the tie set matrix for the figure shown and obtain the network equilibrium equation in the matrix using KVL. Calculate the loop currents and branch voltages. (11)16. (a) What are cut sets? How are they obtained from a graph? (3)(b) Obtain the cut set matrix of the graph shown in figure (7)

17. What is dual? Explain with examples how the dual of the network is obtained (11)18. Explain briefly about the following (a) twig voltages (b) cutest schedules (c) Duality and dual networks (d) link currents (11)

DEPT. OF ECE 14THIAGARAJAN.C-AP/ECE