Electric Current and Ohm's Law

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Senior 1 · Physics

Electric Current and Ohm's Law

5 lessons

Lesson 1 of 5

Electric Current and Potential Difference

23 min

What moves in a wire?

Press the switch by the classroom door and the lights come on at once, even though the switch is metres from the lamps. Nothing seems to travel along the wire, yet something does. In unit 7 you met charges at rest. In this unit, the charges MOVE: a steady flow of charge around a loop of conductors is an electric current, and it is what lights our homes, charges our phones and turns the machines in every workshop in Rwanda.

Activity: making a lamp light

You need a 1.5 V cell in a holder, a small torch lamp in a holder, a switch and three connecting wires.

Join the cell, the switch and the lamp in one loop, as in Figure 1.1, and close the switch. The lamp lights.
Open the switch, or unclip any one wire: the lamp goes out at once.
Close the loop again and turn the cell round: the lamp still lights.

The lamp lights only when there is an unbroken path of conductors from one terminal of the cell, through the lamp, back to the other terminal. Such a path is a closed circuit. A break anywhere makes an open circuit, and the current stops everywhere at once.

Figure 1.1: A simple circuit. By convention, current is drawn from the + terminal to the − terminal; the electrons in the wire actually drift the other way.

Definition

Electric current (symbol $I$ ) is the rate of flow of electric charge:

I = \frac{Q}{t} \qquad \text{or} \qquad Q = It

where $Q$ is the charge in coulombs (C) passing a point in a time $t$ in seconds (s). The SI unit of current is the ampere ( $\mathrm{A}$ ): $1\,\mathrm{A} = 1\,\mathrm{C\,s^{-1}}$ , one coulomb passing each second. Small currents are measured in milliamperes: $1\,\mathrm{mA} = 10^{-3}\,\mathrm{A}$ .

Important

Conventional current and electron flow. Scientists agreed on the direction of current, from + to −, long before the electron was discovered. In a metal wire the moving charges are electrons, which drift from the − terminal to the + terminal. We still draw conventional current from + to −; both descriptions give the same results.

Worked example 1: charge through a lamp

A torch lamp carries a current of $0.25\,\mathrm{A}$ for 2.0 minutes. How much charge passes through it?

Q = It = 0.25\,\mathrm{A} \times (2.0 \times 60)\,\mathrm{s} = 0.25 \times 120 = 30\,\mathrm{C}

Worked example 2: finding a current

A charge of $90\,\mathrm{C}$ flows through a heater in one minute. Find the current.

I = \frac{Q}{t} = \frac{90\,\mathrm{C}}{60\,\mathrm{s}} = 1.5\,\mathrm{A}

How many electrons is that each second? Each second $1.5\,\mathrm{C}$ passes, so

n = \frac{1.5\,\mathrm{C}}{1.6 \times 10^{-19}\,\mathrm{C}} = 9.4 \times 10^{18} \text{ electrons per second}

Potential difference: the push

A current needs something to drive it. A cell or battery does work on the charges: chemical reactions inside it give energy to every coulomb that passes through it. The charges carry that energy round the circuit and give it up in the lamp as light and heat. The energy transferred per coulomb between two points is the potential difference (p.d.) between them, often called the voltage.

A water circuit is a helpful picture: a pump lifts water, which then flows down through a water wheel and turns it.

Electric circuit	Water circuit
cell or battery	pump
charge	water
current (coulombs per second)	rate of flow (litres per second)
potential difference (joules per coulomb)	height difference the pump lifts the water
lamp, where energy is transferred	water wheel
wires	pipes

No water is used up in the wheel, and no charge is used up in the lamp: the same current flows in and out. What is transferred is ENERGY.

Definition

The potential difference $V$ between two points is the work done (energy transferred) $W$ per unit charge that moves between them:

V = \frac{W}{Q} \qquad \text{or} \qquad W = QV

The SI unit is the volt ( $\mathrm{V}$ ): $1\,\mathrm{V} = 1\,\mathrm{J\,C^{-1}}$ . A 1.5 V cell gives $1.5\,\mathrm{J}$ of energy to each coulomb that passes through it; this energy per coulomb given by the source is its electromotive force (e.m.f.).

Worked example 3: energy from a battery

A $12\,\mathrm{V}$ car battery drives $5.0\,\mathrm{C}$ of charge through the headlamp. How much energy is transferred?

W = QV = 5.0\,\mathrm{C} \times 12\,\mathrm{V} = 60\,\mathrm{J}

Worked example 4: current, time and energy together

A $9.0\,\mathrm{V}$ battery drives a current of $0.20\,\mathrm{A}$ through a radio for 5.0 minutes. Find (a) the charge that flows; (b) the energy transferred.

(a) $Q = It = 0.20 \times 300 = 60\,\mathrm{C}$

(b) $W = QV = 60 \times 9.0 = 540\,\mathrm{J}$

Typical currents and voltages

Source	p.d.	Device	Typical current
AA torch cell	$1.5\,\mathrm{V}$	LED indicator light	$20\,\mathrm{mA}$
phone battery	$3.7\,\mathrm{V}$	torch lamp	$0.3\,\mathrm{A}$
car or motorcycle battery	$12\,\mathrm{V}$	phone charging	$1$ to $2\,\mathrm{A}$
mains socket in a Rwandan home	$230\,\mathrm{V}$	electric kettle	about $9\,\mathrm{A}$
high-voltage transmission line	many thousands of volts	lightning flash	about $30\,000\,\mathrm{A}$

Electricity pylons on a hillside in Rwanda. The overhead lines are kept at a very high potential difference so that they can carry energy from power stations to towns over long distances. Photo: roadroid, CC BY-SA 4.0, via Wikimedia Commons

Warning

Common mistakes. (1) Thinking current is "used up" in a lamp: the current leaving a lamp equals the current entering it; only energy is transferred. (2) Mixing up current (the flow, in amperes) and potential difference (the push, the energy per coulomb, in volts). (3) Forgetting to change minutes to seconds in $Q = I t$ .

Tip

Current is the flow of charge (coulombs per second); potential difference is the push (joules per coulomb). Two formulas to learn together: $Q = I t$ and $W = Q V$ .

Where Rwanda's current comes from

Rwanda's national grid, run by Rwanda Energy Group (REG), is fed by hydroelectric stations on rivers such as the Nyabarongo, by power stations that burn methane gas extracted from the deep water of Lake Kivu, and by solar farms such as the one at Rwamagana. Wherever it is made, the energy reaches your home through wires, carried by a current driven by a potential difference of $230\,\mathrm{V}$ at the socket.

Current and potential difference (FuseSchool). Watch the model of charges flowing round a circuit, and how it separates the idea of current (the flow) from potential difference (the energy each charge carries).

✦

Practice

Define electric current and give its SI unit.
A current of $0.50\,\mathrm{A}$ flows through a lamp for 10 minutes. How much charge passes through it?
A charge of $3.0\,\mathrm{C}$ passes a point in a wire in $6.0\,\mathrm{s}$ . Find the current.
How long does it take for $120\,\mathrm{C}$ to flow through a heater carrying $0.40\,\mathrm{A}$ ?
A battery transfers $36\,\mathrm{J}$ of energy to $3.0\,\mathrm{C}$ of charge. What is its potential difference?
How many electrons pass through a wire when a charge of $2.0\,\mathrm{C}$ flows?
Ishimwe says, "The current coming out of a lamp is smaller than the current going in, because the lamp uses some of it up." Evaluate this statement.

Show answersHide answers

The rate of flow of charge, $I = \frac{Q}{t}$ ; unit the ampere (A).
$Q = It = 0.50 \times 600 = 300\,\mathrm{C}$
$I = \frac{3.0}{6.0} = 0.50\,\mathrm{A}$
$t = \frac{Q}{I} = \frac{120}{0.40} = 300\,\mathrm{s}$ , which is 5.0 minutes.
$V = \frac{W}{Q} = \frac{36}{3.0} = 12\,\mathrm{V}$
$n = \frac{2.0}{1.6 \times 10^{-19}} = 1.25 \times 10^{19}$ electrons.
Wrong. Charge is not used up: the current is the same on both sides of the lamp. What the lamp takes is ENERGY from each coulomb, turning it into light and heat, so the potential difference falls across the lamp.

Key points

Current is the rate of flow of charge: $I = \frac{Q}{t}$ , measured in amperes ( $1\,\mathrm{A} = 1\,\mathrm{C\,s^{-1}}$ ).
Conventional current flows from + to −; electrons in a wire drift from − to +.
Potential difference is the energy transferred per coulomb: $V = \frac{W}{Q}$ , measured in volts ( $1\,\mathrm{V} = 1\,\mathrm{J\,C^{-1}}$ ).

Sources and credits

20.1: Current, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Photo: Electricity pylons in Rwanda1.png by roadroid, Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: Current & Potential Difference | Electricity | Physics | FuseSchool, FuseSchool - Global Education, embedded from YouTube.

The activity, the circuit diagram, the analogy table, the worked examples, the Rwandan applications and the practice exercises are written by Ganzaa.

1What moves in a wire?

2Activity: making a lamp light

3Potential difference: the push

4Typical currents and voltages

5Where Rwanda's current comes from

What moves in a wire?

Activity: making a lamp light

Potential difference: the push

Typical currents and voltages

Where Rwanda's current comes from