ac

By:-

DR. VIKRAM SINGHTANUSHREE SINGH

YEAR OF PUBLICATION-2010All rights reserved. No part of this publication may be reproduced,

stored in a retrieval system, transmitted in any form or by any means-

Electronic, Mechanical, Photocopying, Recording or otherwise, without

prior permission of the Authors and Publisher

SAVANT INSTITUTE

TM

CLASS XII

PHYSICS

Physics Alternating current 1

SAVANT EDUCATION GROUP E-17, East of Kailash, New Delhi – 110065. Ph.: +91-11-26224417 www.savantgroup.org

6

ALTERNATING CURRENTSlide 1

An alternating voltage v = vm sin ωt applied to a resistor R

drives a current i = im sin ωt in the resistor, mm

viR

=

The current is in phase with the applied voltage. _____________________ Slide 2 ______________________

For an alternating current i = im sin ωt passing through a resistor R, the average power loss P (averaged over a cycle) due to joule heating is (1/2)i2m R.

To express it in the same form as the dc power (P = I2R), a special value of current is used.

It is called root mean square (rms) current and is denoted

by 00

iI 0.707 i2

= = The mean or average value of

alternating e.m.f. over positive half cycle (0 to T/2) is 0

m 02EE 0.637 E= =π

The average power loss over a

complete cycle is given by P = V I cos φ. The term cos φ is called the power factor. When a value is

given for ac voltage or current, it is ordinarily the rms value. The usual domestic power supply “220 – volt ac” has an rms voltage of 220 V.

The voltage amplitude or peak value is ( )m rmsE 2 E 2 220V 311V= = =

_____________________ Slide 3 ______________________

Wattless current:

Phase angle between Erms and Irms sin φ is π/2, average power consumed in the circuit due to components Irms sin φ is zero. Only the component Irms cos φ which is to actually responsible for consumption of power in an a.c. circuit.

Slide 4

An ac voltage V = Vm sin ωt applied to pure inductor L, drives a current in the inductor i = im sin (ωt – π/2), where im = vm/XL.

XL = ωL is called inductive reactance. The current in the inductor lags the voltage by π/2. The average power supplied to an inductor over one

complete cycle is zero.

Inductor offers no opposition to the flow of d.c. or where as a

resistive path to a.c. An ac voltage V = Vm sin ωt applied to a capacitor drives a current in the capacitor: i = im sin (ωt + π/2). Here.

mm C

c

v 1i , XX C

= =ω

is called capacitive reactance.

f

XC

The current through the capacitor is π/2 ahead of the applied voltage.

As in the case of inductor, the average power supplied to a capacitor over one complete cycle is zero.

In a high frequency A.C. circuit, the capacitor acts like a conductor. In an ac circuit, while adding voltages across different elements, one should take care of their phases properly. For example, if VR and VC are voltages across R and C, respectively in an RC circuit, then the total voltage across RC combination is 2 2

RC R CV V V= + and not VR + VC since

VC is π/2 out of phase of VR.

84 Alternating Current Physics


In a purely inductive or capacitive circuit, cos φ = 0 and no power is dissipated even though a current is flowing in the circuit.

In such cases, current is referred to as a wattles current. _____________________ Slide 5 ______________________

For a series RLC circuit driven by voltage v – vm sin ωt, the current is given by

( )( )

mm m 22

c L

vi i sin t , where iR X X

= ω + φ =+ −

and ( )21 2C LC L

X Xtan Z R X XR

− −φ = = + −

is called impedance of the circuit.

The reciprocal of impedance is called admittance

_____________________ Slide 6 ______________________

An interesting characteristic of a series LCR circuit is the phenomenon of resonance. The circuit exhibits resonance, i.e., the amplitude of the current is maximum at the resonant

frequency, ( )0 L C21 X X .LC

ω = =

The quality factor Q defined by 0

0

L IQR CRω

= =ω

is an

indicator of the sharpness of the resonance, the higher value of Q indicating sharper peak in the current.

(a) When 1LC

ω <ω

, then tan φ is +ve i.e., φ is positive.

In this case, the alternating elm leads the current I by a phase angle φ.

The a.c. circuit is then inductance dominated circuit.

(b) When 1LC

ω <ω

, then tan φ is –ve i.e., φ is negative. In this

case, the alternating e.m.f. lags behind the current I by a phase angle φ. The a.c. circuit is then capacitance dominated circuit.

(c) When 1LC

ω =ω

then tan φ = 0 i.e., φ = 0.

In the case, the alternating e.m.f. and current I are in phase.

The a.c. circuit is then non – inductive _____________________ Slide 7 ______________________

Half power points

On the resonance curve there are two points where power in the circuit is half of the power at resonance.

The 1 0 2 0 0R R Rand (if )2L 2L 2 L

ω = ω − ω = ω + << ω

At lower half power frequency ω1, the circuit is capacitance Xc > XL. At upper half power frequency ω2, the circuit is inductive XL > XC.

_____________________ Slide 8 ______________________

Band Width:

2 1 0 0R R R2L 2L L

⎛ ⎞ ⎛ ⎞∆ω = ω −ω = ω + − ω − =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

The band width is large R and small for small R. The band width ∆ω does nor depends on C in the circuit

(note that resonance frequency ωr does not depends on R while band width depends on R).



Slide 8

Choke coil:

A choke coil is simply an inductor with a large self-inductance and negligible resistance (zero in ideal case).

It is used in A.C. circuits for reducing current without consuming power.

IMPORTANT RESULTS _____________________ Slide 9 ______________________

In LCR series circuit before Resonance (ω < ω0) : Current in the circuit lags in phase by the applied voltage (XL > XC)

_____________________ Slide 10 _____________________

In LCR series circuit after Resonance (ω > ω0) : Current leads is phase by the applied voltage (XC > XL).

_____________________ Slide 11 _____________________

In an AC circuit voltage add according to a formula ( )22 2

R L CV V V V+ − = , where V is the supply voltage, VR

voltage across the resistor, VC voltage across the capacitor. This formula is valid only for rms voltages.

_____________________ Slide 12 _____________________

AC measuring instruments like AC voltmeter, AC ammeter will not have uniform calibration because they measure square of current.

_____________________ Slide 13 _____________________

In LCR circuit the potential difference across an inductor or a capacitor can exceed supply voltage.

_____________________ Slide 14 _____________________

Comparison among Resistance, Reactance and Impedance

Resistance

It is opposition to the flow of any type of current.

Reactance It can be inductive or capacitive opposing the flow of

alternating current.

Impedance It is the total opposition offered to current due to resistance

inductive reactance and capacitive reactance. _____________________ Slide 15 _____________________

Resistance

It is independent on frequency of source of supply. Reactance

It depends on the frequency of the source of supply. Impedance

It depends on the frequency of the source of supply .

Slide 16

Resistance

It is denoted by R and is given by p ( /a)

Reactance It is denoted by XL or XC and is 2πfL or 1/2πfC respectively.

Impedance

It is denoted by Z and is given by ( )22L CZ R X X= + −

_____________________ Slide 17 _____________________

Alternating Voltage

Ideal resistance E = E0 sin ωt Alternating Current I = I0 sin ωt Phase relationship between voltage and current In phase Impedance Z = R Power Loss

2rmsI R

_____________________ Slide 18 _____________________

Alternating Voltage

Ideal inductance E = E0 sin ωt Alternating Current

0I I sin t2π⎛ ⎞= ω −⎜ ⎟

⎝ ⎠

Phase relationship between voltage and current

Current lags by rad or 902π

°

Impedance

Z = XL = ωL = 2πfL Power Loss nil

_____________________ Slide 19 _____________________

Alternating Voltage

Ideal capacitor E = E0 sin ωt Alternating Current

0I I sin t2π⎛ ⎞= ω +⎜ ⎟

⎝ ⎠


Current leads by rad or 902π

°

Impedance

C1 1Z XC 2 fC

= = =ω π

Power Loss nil



Slide 20

Alternating Voltage

Series resistance and inductance

Alternating Current

I = I0 sin (ωt – φ)


Current lags by φ

Impedance

2 2LZ R X= +

Power Loss

rms rmsE I cosφ

_____________________ Slide 21 _____________________

Alternating Voltage Series resistance and capacitance E = E0 sin ωt

Alternating Current I = I0 sin (ωt + φ) Phase relationship between voltage and current Current leads by φ Impedance

2 2CZ R X= +

Power Loss rms rmsE I cosφ

_____________________ Slide 22 _____________________

Alternating Voltage

Series LCR

(i) Mainly inductive E = E0 sin ωt (ii) Mainly capacitive E = E0 sin ωt

Alternating Current I = I0 sin (ωt – φ’) I = I0 sin (ωt + φ’) Phase relationship between voltage and current Current lags by φ’ Current leads by φ’ Impedance

( )22L CZ R X X= + −

( )22C LZ R X X= + −

Power Loss Erms Irms cos φ’ Erms Irms cos φ’

Physics Alternating current

CURRICULUM BASED WORKSHET

Topics for Worksheet – I

Alternating current, R, C, Circuits

Worksheet – I

1. The instantaneous current from an AC source is I = 6 sin 314t. What is the rms value of the current?

2. (a) The peak voltage of an AC supply is 300 V. What is its rms voltage? (b) The rms value of current in an AC circuits 10 A. What is the peak current?

3. A 100 Ω resistor is connected to 220 V, 50 Hz AC supply. Calculate (i) peak potential difference (ii) mean potential difference (iii) rms value of current (iv) net power consumed over a full cycle.

4. An inductor (L = 200 m H) is connected to an AC source of peak elm 210 V and frequency 50 Hz. Calculate the peak current. What is the instantaneous voltage of the source when the current is at its peak value?

5. The peak value of an alternating current 5 A and its frequency is 60 Hz. Find its rms value.

6. If the effective current in a 50 cycle per second AC circuit is 5.0 A, what is (a) the peak value of current? (b)

the value of the current 1300

second after it was zero?

7. A sinusoidal voltage V = 200 sin 314t is applied to a resistor of 10 Ω resistance. Calculate (a) the frequency of the supply (b) the rms value of the voltage (c) the rms value of the current (d) the power dissipated as heat in watt.

8. How much inductance should be connected to 200 V, 50 cycle per second supply so that a maximum current of 0.9 A flows through it?

9. A 100 Hz AC is flowing in a 14 m mH coil. Find its reactance.

Topics for Worksheet – II Inductive circuit, RLC-Circuit Transformer

Worksheet – II

1. Find the maximum value of current when inductance of 2 henry is connected to 150 V, 50 cycle supply.

2. Calculate the value of the current through an inductance of 1 henry and of negligible resistance when connected to an AC source of 200 V and 50 Hz.

3. Calculate the capacitive reactance of a 5 µ F capacitor 6

4. One microfarad capacitor is joined to 200 volt, 50 Hz alternator. Calculate the rms current through capacitor.

5. A 60 µF capacitor is connected to a 110 V, 60 Hz AC supply. Determine the rms value of current in the circuit.

6. A coil of inductance 0.50 H and resistance 100 Ω is connected to a 240 V, 50 Hz AC supply. (a) What is the maximum current in the coil. (b) What is the time lag between the voltage maximum

and current maximum Note: Voltage specification of an AC supply refers to its rms value.

7. A transformer has 200 primary turns and 150 secondary turns. If the primary supply voltage is 230 V, what is the secondary voltage?

8. A transformer has an efficiency of 80% and works at 100 volt and 4kW. If the secondary voltage is 240 V, calculate the primary and secondary currents.

9. A pure inductance of 1 henry is connected across a 110 V, 70 Hz source. Find (a) reactance (b) current (c) peak value of current.

10. A bulb of resistance 10 Ω, connected to an inductor of inductance L, is in series with an AC source marked 100 V, 50 Hz. If the phase angle between voltage and

current is 4π

radian, calculate the value of L.

11. A 100 V, 50 Hz AC source is connected to a series combination of an inductance of 100 mH and a resistance of 25Ω. Calculate the magnitude and phase of the current.

12. When 100 volt DC is applied across a coil, a current of one ampere flows through it. When 100 volt AC of 50 cycle per second is applied to the same coil, only 0.5 ampere flows. Calculate (i) resistance of coil (ii) impedance of coil (iii) inductive reactance of coil (iv) inductance of coil.

13. A Student connects a long sir-cored coil of managing wire to a 100 V DC source and records a current of 1.5 A. When the same coil is connected across 100 V, 50 Hz AC source, the current reduces to 1 A. Calculate the reactance of the coil.

14. A transformer of 100% efficiency has 500 turns in the primary and 10,000 turns in the secondary coil. If the primary is connected to 220 V mains supply, What is the voltage across the secondary coil?

15. A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?

Alternating Current Physics

CURRICULUM BASED CHAPTER ASSIGNMENT

1 Mark Question

1. Peak value of emf of an ac source is E0. What is its rms value?

2. Two identical loops, one of copper and another of constant are removed from a magnetic field within the same time interval. In which loop will the induced current be greater?

3. In a series LCR circuit, the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. What is the phase difference between the applied voltage and the current in the circuit?

4. A coil A is connected to a voltmeter V and the other coil B to an alternating current source D. If a large copper sheet C, is placed between the two coils, how does the induced e.m.f. in the coil A change due to current in the coil B?

5. Draw a graph to show the variation of capacitive reactance with frequency of an ac source.

6. The instantaneous voltage from an ac source is given by E = 300 sin 314 t. what is the rms voltage of the source?

7. What is the phase difference between the voltage across an inductor and a capacitor in an ac circuit?

8. In which direction will the current be induced in the closed loop if the magnet is moved as shown in figure?

9. In a series LCR circuit, the voltages across an inductor, capacitor and resistor are 40 V, 20 V and 20 V respectively. What is the total voltage operative across the combination?

10. The current through the wire PQ is increasing. In which direction does the induced current flow in the closed loop?

2 Mark Question

11. A series LCR circuit with L = 0.12 henry, R = 23 Ω and C = 4.8 × 10–7 F is connected to a variable frequency. At what frequency is the current maximum?

12. A power line feeds input power at 2300 V to a step down transformer with 4000 turns in primary. What should be the number of turns in the secondary to get the output power at 230 V?

13. The effective value of current in an ac circuit is 3A . If the frequency of ac is 50 Hz, what will be the current

1300

s after if is zero?

14. What is the average value of AC during (i) half cycle and (ii) full cycle?

15. An ac current of frequency 50 Hz has rms value of current 10 A. what will be the instantaneous current (1/300) sec after if is zero?

16. Why is radio frequency choke air-cored where as audio frequency choke iron-cored?

17. For an inductance of 2 Henry connected to an ac source of 157V, Hz, find the maximum current through if.

18. If a capacitor is connected in series with LR circuit, what happens to the ac flowing through it? Given reason.

19. How can 11 V ac appliance work with a 220 V ac? Name the device which makes this possible. If a transformer steps down 220 V to 11 V, what is the ratio of the number of turns in the primary to that in the secondary?

20. A 200 km ling telegraph wire has a capacity of 0.014 µF/Km. If its carries an ac of 50 kHz, what should be the value of an inductance required in series so that the impedance is minimum. Take π2 = 10.

21. Obtain the resonant frequency and Q factor of a series of LCR circuit with L = 3.0 H, C = 27 µF and R = 7.4 Ω. It is desired to improve the sharpness of the circuit by reducing the sharpness of the circuit by reducing its full width at half maximum by a factor 2. Suggest a suitable way.

22. Find the maximum current when an inductance coil of one Henry is connected to an ac source of 50 Hz, 200 Volts.

3 Mark Question

23. A capacitor and a resistor are connected in series with an ac source. If the potential difference across C, R are 120 V, 90 V respectively and if the rms current of the circuit is 3 A, calculate the (i) impedance, (ii) power factor of the circuit.

24. An inductor 200 mH, a capacitor C and a resistor 10 ohm are connected in series with a 100 V, 50 s–1 ac source. If the current and voltage are in phase with each other, calculate the capacitance of the capacitor.

25. State the underlying principle of an ac generator. Write the relationship between the peak value and rms value of alternating voltage?

26. State the condition under which the phenomenon of resonance occurs in a series LCR circuit. Plot a graph showing variation of current with frequency of ac source in a series LCR circuit.

27. A coil of inductance, L, a capacitor of capacitance, C, and a resistor of resistance R, are all put in series with an alternating source of emf E (= E0 sin ωt). Write an expression for the (i) total impedance of the circuit. (ii) frequency of the source emf for which the circuit will show resonance.


28. An ac voltage E = E0 sin ωt is applied across an inductor L. obtain an expression for current I.

29. An inductor ‘L’ of reactance XL, is connected in series with a bulb ‘B’ to an ac source as shown in figure Briefly explain how does the brightness of the bulb change, when (i) number of turns of the inductor is reduced and (ii) a capacitor of reactance XC = XL is included in series in the same circuit. ?

30. Calculate the current drawn by the primary of a transformer, which steps down 200 V to 20 V to operate a device of resistance 20 Ω Assume the efficiency of the transformer to be 80%.

31. The output voltage of an ideal transformer, connected to a 240 V ac. mains is 24 V. When this transformer is used to light a bulb with rating 24 V, 24 W, calculate the current in the primary coil of the circuit.

32. A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply. (a) What is the rms value of current in the circuit? (b) What is the net power consumed over full cycle?

5 Mark Question

33. When the series combination of inductance and

resistance are connected with 10 V, 50 Hz ac source, a

current of 1 A flow through the circuit. The voltage

leads current by π/3. Find the resistance and

inductance of the circuit. 34. Define root mean square value of alternating current.

Derive an expression for root mean square value in

terms of peak value of alternating current.

35. Explain with the help of labeled diagram the principle,

construction and working of an alternating current

generator. Derive an expression for the emf induced.

Define the term form factor.

36. Explain with the help of a labeled diagram the principle,

construction and working of a transformer. Derive a

relation between various variables involved. What are

the various energy losses in a transformer? Explain the

role of transformer in long distance transmission of

power?

37. What is meant by impedance? Give its unit. Using a

phasor diagram or otherwise derive the expression for

the impedance of an a.c. circuit containing L, C and R

in series. Find the expression for resonant frequency.

38. For a given ac circuit distinguish between resistance,

reactance and impedance. An ac source of frequency

50 Hz is connected to a 50 mH inductor and bulb. The

bulb glows with some brightness. Calculate the

capacitance of the capacitor to the connected in series

with the circuit, so that the bulb glows with maximum

brightness.

39. Draw the curve showing variation of inductive reactance

and capacitive reactance, with applied frequency of an

ac source.

A capacitor, resistor of 5Ω, and an inductor of 50 mH

are in series with an ac source marked 100V, 50 Hz. It

is found that voltage is in phase with the current.

Calculate the capacitance and the impedance of the

circuit. 40. The frequency of ac is being increased. Explain in effect

of current in each case.

(i)

∼

R

(ii)

∼

L

(iii)

∼

C



QUESTION BANK FOR COMPETITIONS

1. In an LR circuit current at t = 0 is 20 A. After 2s it reduces to 18 A. The time constant of the circuit is: (in second)

(a) 10In9

⎛ ⎞⎜ ⎟⎝ ⎠

(b) 2

(c) 210In9

⎛ ⎞⎜ ⎟⎝ ⎠

(d) 102 In9

⎛ ⎞⎜ ⎟⎝ ⎠

2. Two inductors L1 and L2 are connected in parallel and a time varying current flows as shown. The ratio of currents i1/i2 at any time t is:

i

i1

i2

L1

L2

i

(a) L1/L2

(b) L2/L1 (c) ( )22

1 1 2L / L L+

(d) ( )222 1 2L / L L+

3. Two identical conductors P and Q and placed on two frictionless rails R and S in a uniform magnetic field directed into the plane. If P is moved in the direction shown in figure with a constant speed then rod Q:

× × ×

× × ×

× × ×

P Q

R

S

→B

v

(a) will be attracted towards P

(b) will be repelled away from P

(c) will remain stationary

(d) may be repelled or attracted towards P

4. In L-C oscillation of a circuit, which of the following is true at t = 3T/4 (T = time period of the oscillation). Assume that at t = 0, the capacitor is fully charged?

(a) Energy stored in the inductor is zero, while in capacitor is maximum

(b) Energy in the inductor and capacitor is shared equally

(c) Energy in the inductor is maximum while in the capacitance is zero

(d) None of the above 5. A circular loop of radius 1 m is kept in a magnetic

field of strength 2 T (plane of loop is perpendicular to the direction of magnetic field) Resistance of

the loop wire is 2Ω

πm. A conductor of length 2 m

in sliding with a speed 1 m/s as shown in the figure. Find the instantaneous force acting on the rod: [assume rod has negligible resistance]

(a) 8 N (b) 16 N (c) 32 N (d) 64 N

6. An alternating voltage frequency ω is induced in electric consisting of an inductance L and capacitance C, connected in parallel. Then across the inductance cell:

(a) current is maximum when 2 1LC

ω =

(b) current is minimum when 2 1LC

ω =

(c) voltage is minimum when 2 1LC

ω =

(d) voltage is maximum when 2 1LC

ω =

7. Power factor in series LCR circuit at resonance is: (a) 1

(b) 12

(c) zero (d) infinite



8. The circuit through an inductor of 1 H is given by i = 3t sin t

The voltage across the inductor of 1 H is: (a) 3 sin t + 3 cos t (b) 3 cos t + t sin t (c) 3 sin t + 3t cos t (d) 3t cos t + sin t

9. The electric current in a circuit is given by i = 3t Here, t is in second and i in ampere. The rms current for the period t =0 to t = 1 s is: (a) 3 A (b) 9 A (c) 3 A (d) 3 3 A

10. ω0 the reactance of a certain capacitor equals that of a certain inductor. If the frequency is changed to 2 ω0, what is the ratio of the reactance of the inductor to that of the capacitor? (a) 4 : 1 (b) 2 :1 (c) 1: 2 2 (d) 1 : 2

11. What will be the reading of the voltmeter across the resistance and ammeter in the circuit shown in the figure?

V V V100 V 100 V

A

200V, 50Hz (a) 300 V. 2A (b) 800 V, 2 A (c) 100 V, 2A (d) 200 V, 2 A

12. The voltage of on AC supply varies with time (t) as V = 120 sin 100 πt. The maximum voltage and frequency respectively are (a) 120 V, 100 Hz

(b) 120 V,100Hz2

(c) 60 V, 200 Hz (d) 60 V, 100 Hz.

13. In an AC circuit, the current lags behind the voltage by π/3. The components in the circuit are (a) R and L (b) R and C (c) L and C (d) only R

14. The voltage of an AC source varies with time according to the equation V = 100 sin 100 πt cos 100 πt Where t is in second and V is in volt. The (a) the peak voltage of the source is 100 volt. (b) the peak voltage of the source is 50 volt. (c) the peak voltage of the source is 100 2 volt. (d) the frequency of the source is 50 hertz.

15. A series LCR AC circuit contains L = 8.0 H, C = 0.5 µF, and R = 100 Ω. Then the resonant frequency will be (a) 5 rad s–1 (b) 50 rad s–1 (c) 500 rad s–1 (d) 1500 rad s–1

16. The frequency of AC is 50 Hz. How many time s current becomes zero in one second? (a) 25 times (b) 50 times (c) 100 times (d) 200 times.

17. The potential difference V and current i flowing through an instrument in an AC circuit are given by V = 5 cos ωt volt and i = 2 sin ωt ampere respectively. Then the power dissipated in the instrument is (a) 0 W (b) 2.5 W (c) 5 W (d) 10 W

18. The voltage of AC main is represented by V = 200 2 sin 100 πt volt where t is in second. The frequency of AC is (a) 50 Hz (b) 50 π Hz (c) 100 Hz (d) 100 π Hz



19. A coil of resistance R and inductance L is connected across an ac power supply of rms voltage V. The power dissipated in the coil is (a) V2/R

(b) ( )2 2 2 2V / R L+ ω

(c) ( )2 2 2 2V R / R L+ ω

(d) Zero. 20. A sinusoidal supply of frequency 100 Hz and rms

voltage 12 V is connected to a 2.2. µ F capacitor. What is the rms value of the current? (a) 5.5 µA (b) 2.6 mA (c) 26 µA (d) 17 mA (e) 0.42 mA

21. An LCR circuit contains resistance of 100 ohm and a supply of 200 volt at 300 radian s–1 angular frequency, If only capacitance is taken out from the circuit and the rest of the circuit is joined, current lags behind the voltage by 60°. If on the other hand only inductor is taken out, the current leads by 60° with applied voltage. The current flowing in the circuit is (a) 1 A (b) 1.5 A (c) 2 A (d) 2.5 A

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