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12.4 Electric Potential Difference

Suppose that an electric stove element is connected to a and the element begins to up (Figure 1). If an is connected to the circuit it will measure a fairly large current. You might say that the element is “using elec- tricity,” but what does this mean? What does the element take from the current? To answer these questions, let’s first look at a few analogies. First, imagine a ball held some distance above the surface of Earth, as in Figure 2(a). must have been done on the ball to overcome the gravitational field of Earth and lift it from the ground to its present position, increasing the ball’s gravitational potential . If the ball is then released, the gravitational Figure 1 field will cause it to move back toward Earth, converting gravitational potential The stove element has current passing energy into as the ball falls. through it and it up. What is taken from Now, imagine a small positive charge held at rest a certain distance away from the current to cause the element to heat up? a negatively charged sphere (Figure 2(b)). The negative sphere is surrounded by a field of force, and the positive charge is pulled toward the sphere. Again, work must be done on the small positive charge to overcome this electric force and pull it away (a) from the negative sphere. In this case, the small positive charge has an increase in increase in electric as a result. If released, the positive charge will move back gravitational toward the negative sphere, in much the same way that the ball moved back toward potential Earth, thereby losing electric potential energy. Charged particles moving in the pres- energy of ball ence of an electric field and converting electric potential energy into some other ball form of energy constitute an . Similarly, a current flows in the stove element because an electric field is present that does work on the charges in the circuit, causing them to move. As current passes through the stove element, it experiences opposition to the flow, Earth resulting in a loss of electric potential energy. The energy lost is transferred to the molecules and atoms of the conductor as the current moves through it. This causes the element to heat up and glow—electric potential energy has changed into heat and light energy. + Since the charge loses energy it also loses electric potential, resulting in an electric potential difference (V) between two points, A and B. This can be rep- increase in electric resented as potential energy of positive charge W V = + Q where W is the amount of work that must be done to move a small positive charge, Q, from point A to point B (strictly speaking, this negative gives the electric potential of point B with respect to point A). sphere

The SI unit for electric potential difference is the (V), named after (Figure 3). Figure 2

1 V is the electric potential difference between two points if it takes 1 J of electric potential difference: (V ) the work per to move a positive charge from one point to the other. amount of work required per unit charge to move a positive charge from one point to 1 V = 1 J/C another in the presence of an electric field volt: (V) the SI unit for electric potential dif- ference; 1 V = 1 J/C

442 Chapter 12 12.4

Because of the units in which it is measured, electric potential difference is often referred to as “.”A 12-V car battery is a battery that does 12 J of work on each coulomb of charge that flows through it. Electric potential difference between two points in a circuit is measured with a device called a voltmeter.To measure electric potential difference, a voltmeter is connected across the source and the bulb in the circuit (Figure 4). This type of connection is called a parallel connection. The lost or work done by a charge, Q, going through a potential difference, V, can be written

E = QV

Since it is often easier to measure the current and the time during which it lasts, we can use the equation

Q = It and, substituting in the first equation, we get Figure 3 E = VIt Alessandro Volta (1745–1827). After a child- hood showing little promise as a scholar, as an expression for the electrical energy lost by a current, I, through a potential Volta forged ahead, becoming professor of difference, V, for a time interval, t. physics at the high school in Como, . His first major contribution was the discovery of Voltmeter measures the electrophorus, a device capable of pro- ducing and storing a large electrical charge. potential drop. 1.5 His reward was a professorship at the and membership in the Royal Society. Volta’s most significant – + achievement was the invention of the first using bowls of salt solution connected by arcs of metal with copper at one end and tin or at the other. For this inven- tion, Napoleon awarded him the medal of the Legion of Honour and made him a Count.

light bulb voltmeter: a device that measures electric potential difference between two points in a circuit cell or battery 1.5

– + Voltmeter measures potential rise. –+

Figure 4 Measuring potential differences with a volt- meter connected in parallel

Electricity 443 Sample Problem 1 A 12-V car battery supplies 1.0 × 103 C of charge to the starting motor. How much energy is used to start the car?

Solution V = 12 V Q = 1.0 × 103 C E = ?

E =QV = (1.0 × 103 C)(12 V) E = 1.2 × 104 J

The amount of energy used to start the car is 1.2 × 104 J.

Sample Problem 2 If a current of 10.0 A takes 3.0 × 102 s to boil a kettle of water requiring DID YOU KNOW ? 3.6 × 105 J of energy, what is the potential difference (voltage) across the kettle? Neurons in the Human Body An important part of the body’s nervous Solution system is the neuron, a nerve cell that can I = 10.0 A receive, interpret, or transmit electrical mes- t = 3.0 × 102 s sages. An electric potential difference exists across the surface of every neuron because E = 3.6 × 105 J of a greater number of negative charges on V = ? the inside than on the outside. The potential E difference is typically about 60 mV to 90 mV. V = It 3.6 × 105 J = (10.0 A) (3.0 × 102 s) V = 1.2 × 102 V

There is a potential difference of 1.2 × 102 V across the kettle.

Practice

Understanding Concepts Answers 1. A hair dryer has 1.2 × 103 C of charge passing through a point in its 1. 1.4 105 J circuit when it is connected to a 120-V supply. How much energy is used by the hair dryer? 3. 9.0 105 J 2. Write an equation for each of the following: (a) charge in terms of energy used and voltage (b) voltage in terms of charge and energy used 3. A light bulb operating on an electric current of 0.83 A is used for 2.5 h at an electric potential difference of 120 V. How much energy is used by the light bulb?

444 Chapter 12 12.4

4. Write an equation for each of the following: Answers (a) electric current in terms of energy used, voltage, and time interval 5. 2.8 A (b) voltage in terms of electric current, energy used, and time interval 6. 3.6 103 s (c) time interval the device is used in terms of current, voltage, and energy used 5. A 120-V electric sander operating for 5.0 min uses 1.0 × 105 J of energy. Find the current through the sander. 6. An electric can opener used in a 120-V circuit operates at 2.2 A using 9.5 × 105 J of energy all year. How long was the can opener used for that year?

SUMMARY Electric Potential Difference • Electric potential difference (V) is the amount of work required per unit charge to move a positive charge from one point to another in the presence of an electric field. • The electric potential difference (V) between two points, A and B, is repre- W V = sented by the equation Q . • Because of the units in which it is measured, electric potential difference is often referred to as “voltage.” • The electrical energy lost by a current, I, through a potential difference, V, for a time, t, is represented by the equation E = VIt.

Section 12.4 Questions

Understanding Concepts 1. What amount of energy does a kettle use to boil water if it has 810 C of charge passing through it with a potential difference of 120 V? 2. What is the potential difference across a if 75 C of charge transfers 9.0 103 J of energy to the compressor motor? 3. An electric baseboard heater draws a current of 6.0 A and has a potential difference of 240 V. For how long must it remain on to use 2.2 105 J of electrical energy? 4. A flash of lightning transfers 2.0 109 J of electrical energy through a potential difference of 7.0 107 V between a cloud and the ground. Calculate the quantity of charge transferred in the lightning bolt. 5. Calculate the energy stored in a 9.0 V battery that can deliver a continuous current of 4.0 mA for 2.0 103 s. 6. If a charge of 0.30 C moves from one point to another in a con- ductor and, in doing so, releases 5.4 J of electrical energy, what is the potential difference between the two points? 7. Describe the significance of two points in a conductor that are at the same electric potential. How much work must be done to move a charge between the two points? (continued)

Electricity 445 8. How are electric potential energy and gravitational potential energy different and how are they similar? 9. Using the definition of a volt, compare a 6.0-V battery with a 12.0-V battery. 10. Compare and contrast the methods used to connect and voltmeters to electric circuits.

Applying Inquiry Skills 11. An electric current passes through a heating element on a stove. The element heats up and begins to glow. Discuss the energy transformations involved. How is the law of conservation of circuit: a path for electric current energy involved in these energy transformations? 12. Gravitational potential energy has been used as an analogy in load: any device in a circuit that transforms understanding electric potential difference between a small posi- electrical potential energy into some other form tive charge and a negative sphere. Will the analogy be as useful of energy, causing an electric potential drop if both charges have the same sign?

wire with electric current back to 12.5 Kirchhoff’s Laws

light bulb (load) for Electric Circuits + – Electrons possess electric potential energy that can be transformed into heat, light, and motion. For such transformations to occur, we need to connect a source of electric potential energy to one or more components by means of a circuit, which is a path for electric current. Any component or device in a circuit dry cell that transforms electric potential energy into some other form of energy, causing (source of wire with electric an electric potential drop, is called a load. electric potential) current to light bulb The simple circuit in Figure 1 provides a complete path for the electric cur- rent. The path can be traced from the positive terminal of the dry cell through Figure 1 the light bulb, and back to the negative terminal of the dry cell. As electric A simple electric circuit charges go through this simple circuit, they transfer the electric potential energy they acquired from the dry cell to the light bulb. In a sense, then, the charges act as carriers of energy from the source of electrical energy (the dry cell) to the con- verter of electrical energy (the light bulb). Electric current can go through a circuit only if the circuit provides a com- plete path. Any break in the circuit will cause the electric current to cease. The circuit is then said to be an open circuit. If, by chance, two wires in a circuit touch, so that charge can pass from one wire to the other and return to the negative ter- minal of the source without passing through the load, the circuit is said to be a , or, simply, a “short.” Circuit Symbols The various paths through a circuit can be complex and they can contain many Figure 2 different types of electrical devices and connectors (Figure 2). To simplify The Intel Pentium micro-processor contains descriptions of these paths, circuit diagrams are drawn, using symbols that show thousands of electric circuits on a silicon chip exactly how each device is connected to the others. The components of an elec- the size of a fingernail and can process hun- dreds of millions of instructions per second. tric circuit are called elements, and the symbols most commonly used in such schematic diagrams are displayed in Figure 3. elements: the components of an electric circuit

446 Chapter 12