Electric Circuits Voltage, Resistance and Power. Voltage Volt – Unit of electrical pressure A VOLTAIC CELL may be described as a means of converting chemical.

Electric Circuits

Voltage, Resistance and Power

Voltage• Volt – Unit of electrical pressure• A VOLTAIC CELL may be described

as a means of converting chemical energy into electrical energy.

• If a load, such as a light, is connected to the cell, a current will flow and the light will glow. As the cell is used, the chemical action continues until the zinc electrode is consumed. The chemical equation for this action would be:

• Zn + H2 SO4 + H2OZnSO4 + H20 + H2

• Zinc plus sulfuric acid plus water chemically reacts to form zinc sulfate and water and free hydrogen gas. This cell cannot be recharged because the zinc has been consumed. It is called a PRIMARY CELL. The chemical action cannot be reversed.

• Mercury batteries are rechargeable, they are called secondary cells.

• Batteries use chemicals to make energy (Chemical Energy) and generators use movement to make energy (Mechanical Energy).

Theory of VoltageElectrical potential energy is useful in solving problems, particularly those involving charged particles. But at any point in an electric field, as the value of the charge increases, the value of the electrical potential energy increases. The electric potential at some point is defined as the electrical potential energy associated with a charged particle in an electric field divided by the charge of the particle.

Although a greater charge will involve a greater amount of electrical potential energy, the ratio of that energy to the charge is the same as it would be if a smaller charge were at the same position in the field. In other words, the electric potential at a point is independent of the charge at that point.

TheoryPotential difference is a measure of the change in the electrical potential energy divided by the charge. The SI unit for potential difference (and electric potential) is the volt, V, and is equivalent to one joule per coulomb. As a 1 C charge moves through a potential difference of 1 V, the charge gains (or loses) 1 J of energy. The potential difference between the two terminals of a battery, for instance, can range from about 1.5 V for a small battery to about 12 V. The potential difference between the two slots in a household electrical outlet is about 120 V. Remember that only electrical potential energy is a quantity of energy, with units in joules. Electric potential and potential difference are both measures of energy per unit charge (measured in units of volts), and potential difference describes a change in energy per unit charge.

The value of e has since been determined to be 1.602 19 x 10-19 C, where the coulomb (C) is the SI unit of electric charge. A total charge of —1.0 C contains 6.2 X 1018 electrons (e). Comparing this with the number of free electrons in 1 cm3 of copper, which is on the order of 1023, shows that 1.0 C is a substantial amount of charge.

Battery Voltages• Batteries in Series- In Fig. 2-8,

four cells are connected in SERIES. The output voltage will equal,

• V =V x n,• V = 1 .5 volts x 4 = 6 volts Out• Notice that the voltage has

increased four times, however, the capacity of the battery to supply a current is the same as one cell.

• Batteries in Parallel – In Fig. 2-9 the batteries have been connected together. These cells are connected in PARALLEL. The total voltage across the terminals of the battery is the same as one cell only. Although the voltage has not increased, the life of the battery has been increased because the current is drawn from all cells instead of one.

Current• Current is the rate of charge movement• A current exists whenever there is a net

movement of electric charge through a medium. To define current more precisely, suppose positive charges are moving through a wire. The current is the rate at which these charges move through the cross section of the wire. If ΔQ is the amount of charge that passes through this area in a time interval, Δt, then the current, I, is the ratio of the amount of charge to the time interval. Current can be direct or alternating

• There are two different types of current: direct current (dc) and alternating current (ac). In direct current, charges move in only one direction. In alternating current, the motion of charges continuously changes in the forward and reverse directions. In alternating current, the terminals of the source of potential difference are constantly changing sign. Hence, there is no net motion of the charge carriers in alternating current; they simply vibrate back and forth.

Resistance

• RESISTANCE is the opposition to electric current in a conducting wire or material. A large wire can carry more electrons than a small wire. It has less resistance to the flow, because of its larger size.

• Resistance depends on size and material.

Ohms LawOHM’S LAWOne of the fundamental laws of electrical circuits was derived from experimentation done by

George Simon Ohm, the German scientist and philosopher, during the 19th century. To honor the achievements of Mr. Ohm, the standard unit of measurement for resistance is called the OHM. It is frequently represented by the Greek letter “omega” as . If you see on a diagram 1000 c , it means 1000 ohms. In electronic circuits the use of the kilohm and megohm is very common. The Greek prefix “kilo” means 1000. The prefix “meg” means one million. These are summarized in Table 3-2.

Ohm’s Law is stated as: The current in amperes in a circuit is equal to the applied voltage divided by the resistance, or,

I (in amperes) = E (in volts)/ R (in ohms)Notice the letter symbols used in this equation:I = intensity of the current in amperesE = electromotive force in voltsR = resistance in ohmsIn non-mathematical language this formula means:As voltage is increasedAs voltage is decreasedAs resistance is increasedAs resistance is decreased— current increases— current decreases— current decreases-— current increases

Using Ohms Law

Series Circuits• SERIES CIRCUITS• If a circuit is so arranged that all

of the current flowing in the circuit will pass through all components, these components are connected in SERIES.

• As current passes through a resistor, a certain amount of energy is used and a certain amount of pressure or voltage is lost. The voltage loss across each resistor may be calculated by Ohm’s Law, using formula, E(V) = I x R,

Series Circuits….Kirchhoff’s Laws

• Since these resistors are connected in series, all the current flowing in the circuit must pass through each resistor. Therefore, current is the same in all parts of the circuit.

• 1. The sum of the voltage drops around a series circuit will equal the source voltage.

• 2. The current is the same when measured at any point in the series circuit.

Parallel Circuits

• When several components are connected to the same voltage source, the components are connected in parallel or “side by side.” Multiple paths for current flow are provided by a parallel circuit, because each resistor constitutes a path of its own.

When equal resistors are connected in parallel, the total resistance of the parallel network is equal to any one resistor divided by the number of resistors in the network.

The applied voltage is the same for each resistor, because each is connected across the same voltage source.Therefore, the currents are, using Ohm’s

The total current flowing through the network would be the sum of the individual branch currents or:

.2 + .2 + .2 = .6 amps

Parallel Circuits…

Summarizing • The voltage across all branches of a parallel

network is the same.• The total current is equal to the sum of the

individual branch currents.• The total resistance of any parallel circuit must

always be less than the value of’ any resistor in the network..

• The branch of the circuit containing the greatest resistance conducts the least current.

Parallel Circuits…Multiple resistors with different values.

• The conductance of a circuit is equal to the sum of the conductances of the branch circuits.

• Sum the 1/R of the resistances and then recipicate the answer.

Power• In any electrical circuit, the only component in the circuit

that uses electrical power is resistance. POWER is the time rate of doing work. In the physics of machines it is discovered that when a force moves through a distance, work is done. For example, if a 10 lb. weight is lifted one foot, the work done equals,

• F (force) x D (distance) or 10 x 1 = l0ft. lb. of work.• No reference is made to time in this equation. One might

take five seconds or 10 minutes to lift the 10 pound weight. However, if one lifted the 10 pound weight at the rate of once each second, then the power expended would be 10 ft. lb. per second. To carry the example one step further, if one lifted the 10 pound weight in one-half or .5 second, then the power expended would equal: 10/5 or 20 ft. lb. per second.

In electricity the unit of power is the watt, named in honor of James Watt, who is credited with the invention of the steam engine. When one volt of electrical pressure moves one coulomb of electricity in one second, the work accomplished is equal to one watt of power. Recall the definition of one ampere — when one coulomb of electrons moves past a given point in a circuit in one second. So power in an electrical circuit is equal to:

P (watt) = E (volts) x I (amperes)• Use these figures when comparing electrical power to

mechanical power:• 746 watts = I horsepower• The power formula, sometimes called Watt’s law, can be

arranged algebraically, so that if two quantities are known, the third unknown may be found.

Example: A circuit with an unknown load has an applied voltage of 100 volts. The measured current is 2 amperes. How much power is consumed?

P = I x E or 2amps x I00V = 200W

Example: An electric toaster rated at 550 watts is connected to a 11 0 volt source. How much current will this appliance use?

Power and Circuits• POWER IN A SERIES CIRCUIT• As the voltage overcomes the

resistance, work is done and power is the time rate of doing work. Referring to the section on power, earlier in this chapter, you will discover that in electricity, P = I x E. The energy lost in overcoming the resistance takes the form of heat. This must be dissipated by the resistor into the surrounding air. This explains why some resistors are larger than others. They must be large enough to provide radiation surface for heat dissipation.

Formulas

If you have two of the four variables you can solve for the others.