Charge, current, voltage and power

Key ideas

An electric current is a flow of charge. Voltage measures the energy given to (or taken from) each coulomb of charge. Power is how fast energy is transferred.

Current is flowing charge

$I = \frac{q}{t}$

$I$ — current (A)
$q$ — charge that flows (C)
$t$ — time (s)

One amp is one coulomb of charge passing each second.

Voltage is energy per charge

$V = \frac{\Delta E}{q}$

$V$ — voltage / potential difference (V)
$\Delta E$ — energy transferred (J)
$q$ — charge (C)

One volt means one joule delivered to each coulomb.

Power in a circuit

Power is energy transferred per second, and for an electrical component it equals voltage times current:

$P = IV \qquad P = \frac{\Delta E}{t}$

$P$ — power (W)
$I$ — current (A), $V$ — voltage (V)
$\Delta E$ — energy transferred (J) in time $t$ (s)

:::tip Voltage is per coulomb, not total energy. If a component transfers $60$ J while $3$ C passes through, the voltage is $\Delta E / q = 60/3 = 20$ V, not $60$ V. Always divide the energy by the charge. :::

Worked ExampleCharge, energy and power from a torch bulb

A torch bulb runs a current of $0.50$ A from a $3.0$ V battery for $2.0$ minutes. Find the charge that flows, the power, and the total energy transferred.

Step 1 — Convert time and find the charge

$t = 2.0 \text{ min} = 120 \text{ s}$ $q = It = 0.50 \times 120 = 60 \text{ C}$

Step 2 — Power

$P = IV = 0.50 \times 3.0 = 1.5 \text{ W}$

Step 3 — Energy (power × time)

$\Delta E = Pt = 1.5 \times 120 = 180 \text{ J}$

Practice question

A device draws $2.0$ A at $12$ V. How much energy does it transfer in $30$ s?

Worked solution: $P = IV = 2.0 \times 12 = 24$ W, so $\Delta E = Pt = 24 \times 30 = 720$ J.

Test yourself

Practice by grade

One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.

Achieved

A current of $3.0$ A flows for $20$ s.

Calculate the charge that passes.

Merit

A heater transfers $9000$ J of energy in $30$ s while connected to a $12$ V supply.

Calculate the power and the current drawn.

Excellence

Two appliances are connected to the same $230$ V mains supply. Appliance A draws $2.0$ A, appliance B draws $8.0$ A. Explain fully, with calculations, which transfers more energy in one hour and why.

Charge, current, voltage and power

Covers AS91173

Key ideas

An electric current is a flow of charge. Voltage measures the energy given to (or taken from) each coulomb of charge. Power is how fast energy is transferred.

Current is flowing charge

$I = \frac{q}{t}$

$I$ — current (A)
$q$ — charge that flows (C)
$t$ — time (s)

One amp is one coulomb of charge passing each second.

Voltage is energy per charge

$V = \frac{\Delta E}{q}$

$V$ — voltage / potential difference (V)
$\Delta E$ — energy transferred (J)
$q$ — charge (C)

One volt means one joule delivered to each coulomb.

Power in a circuit

Power is energy transferred per second, and for an electrical component it equals voltage times current:

$P = IV \qquad P = \frac{\Delta E}{t}$

$P$ — power (W)
$I$ — current (A), $V$ — voltage (V)
$\Delta E$ — energy transferred (J) in time $t$ (s)

Worked ExampleCharge, energy and power from a torch bulb

A torch bulb runs a current of $0.50$ A from a $3.0$ V battery for $2.0$ minutes. Find the charge that flows, the power, and the total energy transferred.

Step 1 — Convert time and find the charge

$t = 2.0 \text{ min} = 120 \text{ s}$ $q = It = 0.50 \times 120 = 60 \text{ C}$

Step 2 — Power

$P = IV = 0.50 \times 3.0 = 1.5 \text{ W}$

Step 3 — Energy (power × time)

$\Delta E = Pt = 1.5 \times 120 = 180 \text{ J}$

Practice question

A device draws $2.0$ A at $12$ V. How much energy does it transfer in $30$ s?

Worked solution: $P = IV = 2.0 \times 12 = 24$ W, so $\Delta E = Pt = 24 \times 30 = 720$ J.

Test yourself

Practice by grade

One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.

Achieved

A current of $3.0$ A flows for $20$ s.

Calculate the charge that passes.

Merit

A heater transfers $9000$ J of energy in $30$ s while connected to a $12$ V supply.

Calculate the power and the current drawn.

Excellence

Two appliances are connected to the same $230$ V mains supply. Appliance A draws $2.0$ A, appliance B draws $8.0$ A. Explain fully, with calculations, which transfers more energy in one hour and why.