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BIG IDEA

Electric currents carry electrical energy that can be transformed into other forms of energy.

Electric Current

MAIN IDEA

Electric current is the flow of electric charges.

Essential Questions

What is electric current?

How can you think about energy in electric circuits?

What is Ohm’s law?

How are power, current, potential difference, and resistance mathematically related?

Review Vocabulary

• electric potential difference: the work done moving a positive test charge between two points in an electric field divided by the magnitude of that test charge

New Vocabulary

• Electric current

  • Conventional current

  • Battery

  • Electric circuit

  • Ampere

• Resistance

• Resistor

• Parallel connection

• Series connection

Energy Transfer in Electric Circuits

• Flowing water at a waterfall has potential and kinetic energy.

• Electrical energy transfers large amounts of energy efficiently over long distances (e.g., power lines at high voltages).

• Electric energy can be converted into sound, light, heat, motion, etc.

Producing Electric Current

• This transfer is usually done at high potential differences through power lines.

• Once this energy reaches the consumer, it can easily be converted into another form or combination of forms, including sound, light, thermal energy, and motion.

• Because electric energy can so easily be changed into other forms, it has become indispensable in our daily lives.

Producing Electric Current (cont.)

• When two conducting spheres touch, charges flow from the sphere at a higher potential to the one at a lower potential.

• The flow continues until there is no potential difference between the two spheres.

• A flow of charged particles is an electric current.

Producing Electric Current (cont.)

• In the figure, two conductors, A and B, are connected by a wire conductor, C.

• Charges flow from the higher potential difference of B to A through C.

• The flow stops when the potential
  difference between A, B, and C
  is zero.

• The direction in which a positive test charge moves is called conventional current.

Producing Electric Current (cont.)

• Usually, it is the negative charges (electrons) that flow. The flow of electrons and the direction of the conventional current are in opposite directions.

• You could maintain the electric potential difference between B and A by pumping charged particles from A back to B, as illustrated in the figure.

• Since the pump increases the
  electric potential energy of the
  charges, it requires an external
  energy source to run.

• This energy could come from a
  variety of sources.

Producing Electric Current (cont.)

• One familiar source, a voltaic or galvanic cell (a common dry cell), converts chemical energy to electric energy.

• A battery is made up of several galvanic cells connected together.

• A second source of electric energy— a photovoltaic cell, or solar cell—changes light energy into electric energy.

Producing Electric Current (cont.)

• The charges in the figure
  move around a closed
  loop, cycling from pump B,
  through C to A, and back
  to the pump.

• Any closed loop or
  A conducting path allowing electric charges to flow is called an electric circuit.

• A circuit includes a charge pump, which increases the potential energy of the charges flowing from A to B, and a device that reduces the potential energy of the charges flowing from B to A.

Electric Circuits

• The potential energy lost by the charges, qV, moving through the device is usually converted into some other form of energy.

• For example, electric energy is converted to kinetic energy by a motor, to light energy by a lamp, and to thermal energy by a heater.

• A charge pump creates the flow of charged particles that make up a current.

• Charges cannot be created or destroyed, but they can be separated.

• Thus, the total amount of charge—the number of negative electrons and positive ions—in the circuit does not change.

• If one coulomb flows through the generator in 1 s, then one coulomb also will flow through the motor in 1 s.

• Thus, charge is a conserved quantity.

• Energy is also conserved.

• The change in electric energy, ΔE, equals qV. Because q is conserved, the net change in potential energy of the charges going completely around the circuit must be zero.

• The increase in potential difference produced by the generator equals the decrease in potential difference across the motor.

• Power, which is defined in watts, W, measures the rate at which energy is transferred.

• If a generator transfers 1 J of kinetic energy to electric energy each second, it is transferring energy at the rate of 1 J/s, or 1 W.

• The energy carried by an electric current depends on the charge transferred, q, and the potential difference across which it moves, V.

Thus, E = qV.

Rates of Charge Flow and Energy Transfer

• The unit for the quantity of electric charge is the coulomb.

• The rate of flow of electric charge, q/t, called electric current, is measured in coulombs per second.

• Electric current is represented by I, so I = q/t.

• A flow of 1 C/s is called an ampere, A.

• The energy carried by an electric current is related to the voltage, E = qV.

• Since current, I = q/t, is the rate of charge flow, the power, P = E/t, of an electric device can be determined by multiplying voltage and current.

Rates of Charge Flow and Energy Transfer (cont.)

• To derive the familiar form of the equation for the power delivered to an electric device, you can use P = E/t and substitute E = qV and q = It

Power P = IV

• Power is equal to the current times the potential difference.

Rates of Charge Flow and Energy Transfer (cont.)

• An electric circuit is drawn using standard symbols for the circuit elements.

• Such a diagram is called a circuit schematic. Some of the symbols used in circuit schematics are shown below.

Diagramming Circuits

• An artist’s drawing and a schematic of the same circuit are shown below.

Diagramming Circuits (cont.)

• An ammeter measures current and a voltmeter measures potential differences.

• Each instrument has two terminals, usually labeled
  + and –. A voltmeter measures the potential difference across any component of a circuit.

• When connecting the voltmeter in a circuit, always connect the + terminal to the end of the circuit component that is closer to the positive terminal of the battery, and connect the – terminal to the other side of the component.

Diagramming Circuits (cont.)

• Suppose two conductors have a potential difference between them.

• If they are connected with a copper rod, a large current is created.

• On the other hand, putting a glass rod between them creates almost no current.

• The property determining how much current will flow is called resistance.

Resistance and Ohm’s Law

• The table lists some of the factors that impact resistance.

• Resistance is measured by placing a potential difference across a conductor and dividing the voltage by the current.

• The resistance, R, is defined as the ratio of electric potential difference, V, to the current, I.

• Resistance is equal to voltage divided by current.

• The resistance of the conductor, R, is measured in ohms.

Resistance

Resistance and Ohm’s Law (cont.)

• The unit for resistance is named for German scientist Georg Simon Ohm, who found that the ratio of potential difference to current is constant for a given conductor.

• The resistance for most conductors does not vary as the magnitude or direction of the potential applied to it changes.

• A device having constant resistance independent of the potential difference obeys Ohm’s law.

Resistance and Ohm’s Law (cont.)

• Most metallic conductors obey Ohm’s law, at least over a limited range of voltages.

• Many important devices, such as transistors and diodes in radios and pocket calculators, and lightbulbs do not obey Ohm’s law.

• Wires used to connect electric devices have low resistance.

• A resistor is a device designed to have a specific resistance.

• Resistors may be made of graphite, semiconductors, or wires that are long and thin.

Resistance and Ohm’s Law (cont.)

Controlling Current

• There are two ways to control the current in a circuit.

• Because I =V/R, I can be changed by varying V, R, or both.

• Current can be controlled by adjusting voltage (V), resistance (R), or both.

• Example:

  • To reduce current from 0.2 A to 0.1 A in a circuit with (V=6V) and (R=30 \Omega), either:

    • Lower voltage to 3 V, or

    • Increase resistance to 60 Ω.

Resistance and Ohm’s Law (cont.)

• Resistors often are used to control the current in circuits or parts of circuits.

• Sometimes, a smooth, continuous variation of the current is desired.

• For example, the speed control on some electric motors allows continuous, rather than step-by-step, changes in the rotation of the motor.

Resistance and Ohm’s Law (cont.)

• To achieve this kind of control, a variable resistor, called a potentiometer, is used.

• A circuit containing a potentiometer is shown in the figure.

Resistance and Ohm’s Law (cont.)

Variable Resistors (Potentiometers)

• Used for smooth control of current, e.g., motor speed, volume, brightness.

• Consist of a coil of resistance wire and a sliding contact to vary resistance continuously.

• Increasing wire length in circuit increases resistance, lowering current.

• In this way, the speed of a motor can be adjusted from fast, with little wire in the circuit, to slow, with a lot of wire in the circuit.

• Other examples of using variable resistors to adjust the levels of electrical energy can be found on the front of a TV: the volume, brightness, contrast, tone, and hue controls are all variable resistors.

Resistance and Ohm’s Law (cont.)

• Dry skin has high resistance, reducing current flow.

• Wet skin lowers resistance, increasing current and danger.

• Currents as low as 1 mA can be felt; 15 mA can cause muscle loss of control; 100 mA can be fatal.

Resistance and Ohm’s Law (cont.)

Current Through a Resistor

A 30.0-V battery is connected to a 10.0-Ω resistor. What is the current in the circuit?

Step 1: Identify the known and unknown variables.

Known:

V = 30.0 V

R = 10 Ω

Unknown:

I = ?

Step 2: Solve for the Unknown

Use I = V/R to determine the current.

Substitute V = 30.0 V, R = 10.0 Ω

• When a voltmeter is connected across another component, it is called a parallel connection because the circuit component and the voltmeter are aligned parallel to each other in the circuit, as diagrammed in the figure.

Parallel and Series Connections

• An ammeter measures the current through a circuit component.

• The same current going through the component must go through the ammeter, so there
  can be only one current path.

• A connection with only
  one current path is called
  a series connection.

What is an electric current?

Section Check

An electric current is a flow of charged particles. It is measured in C/s, which is called an ampere, A.

Answer

In a simple circuit, a potential difference of 12 V is applied across a resistor of 60 Ω and a current of 0.2 A is passed through the circuit. Which of the following statements is true if you want to reduce the current to 0.1A?

A. Replace the 60-Ω resistor with a 30-Ω resistor.

B. Replace the 60-Ω resistor with a 120-Ω resistor.

C. Replace the potential difference of 12 V by a potential difference of 24 V.

D. Replace the 60-Ω resistor with a 15-Ω resistor.

Reason: There are two ways to control the current in a circuit. Because I = V/R, I can be changed by varying V, R, or both.

According to Ohm’s law, the greater the resistance of the resistor, the smaller the current passing through it. In order to halve the current passing through a resistor, the resistance of the resistor must be doubled. Hence, to reduce the current to 0.1 A, the 60- resistor must be replaced with a 120- resistor.

Answer

A 12-V battery delivers a 2.0-A current to an electric motor. If the motor is switched on for 30 s, how much electric energy will the motor deliver?

A.

B.

C.

D

Reason: Energy is equal to the product of power and time.

That is, E = Pt.

Also, power is equal to the product of current and potential difference.

That is, P = IV.

Therefore, E = IVt = (2.0 A) (12 V) (30 s).

Energy is measured is Joules (J).

Answer

• Electric current is a flow of charged particles. By convention, current direction is the direction in which positive test charge moves.

• A circuit transforms electrical energy to thermal energy, radiant energy or some other form of energy.

• Ohm’s law states that the ratio of potential difference to current is a constant for a given conductor. Any resistance that does not change with potential difference or the direction of charge flow obeys Ohm’s law.

Current and Circuits

Study Guide

The following equations show how power, current, potential difference and resistance are mathematically related.

P = IV