2.20-2.21 - Energy transferred by charge and voltage

2.20-2.21 - Energy transferred by charge and voltage

Voltage tells you how much energy is transferred for each coulomb of charge that passes through part of a circuit. This lesson keeps that idea precise: one volt means one joule per coulomb, and the total energy transferred depends on both the charge that passes and the voltage across the component.

Voltage as energy per coulomb

In a circuit, charge can transfer energy as it passes through a component. In a lamp, energy is transferred electrically to the lamp and then by light and heating to the surroundings. In a motor, energy is transferred to kinetic and thermal energy stores. In a resistor, energy is mainly transferred by heating.

The voltage across a component tells you the energy transferred by each coulomb of charge that passes through that component. For a cell or battery it works the other way round: its voltage tells you the energy transferred to each coulomb of charge that passes through it.

Voltage

Voltage is the energy transferred per unit charge passed.

"Per unit charge" means "for each coulomb of charge". If a component has a voltage of 3 V across it, then each coulomb of charge passing through the component transfers 3 J of energy.

Voltage is not the same thing as energy. Voltage is energy transferred per coulomb. The total energy transferred also depends on how much charge passes.

For example, a 6 V lamp transfers 6 J of energy for each 1 C of charge that passes through it. If 4 C of charge passes through the lamp, the total energy transferred is four lots of 6 J: 4×6=244 \times 6 = 24 J.

The volt as joule per coulomb

The unit of voltage is the volt, symbol V. The unit of energy is the joule, symbol J. The unit of charge is the coulomb, symbol C.

Because voltage is energy transferred per unit charge:

voltage=energy transferredcharge\text{voltage} = \frac{\text{energy transferred}}{\text{charge}}

So one volt is one joule per coulomb:

1 V=1 J/C1\text{ V} = 1\text{ J/C}

This unit meaning is often the quickest way to interpret a voltage value.

Voltage across a componentMeaning
1 V1 J is transferred by each 1 C of charge
2 V2 J are transferred by each 1 C of charge
12 V12 J are transferred by each 1 C of charge

Do not read "12 V" as "12 J in total". It means 12 J per coulomb. The total energy is larger if more charge passes.

Using E = QV

The total energy transferred is found by multiplying the charge that passes by the voltage.

Energy transferred by charge and voltage

E=Q×VE = Q \times V

In this equation:

SymbolQuantityUnit
EEenergy transferredjoule, J
QQchargecoulomb, C
VVvoltagevolt, V

Learn this equation. It is not given in the exam, either in this form or rearranged.

The equation matches the meaning of the volt. If 1 C transfers 3 J, then 5 C transfers five times as much:

E=Q×V=5×3=15 JE = Q \times V = 5 \times 3 = 15\text{ J}

Worked example: A charge of 8.0 C passes through a 4.5 V lamp. Calculate the energy transferred by the lamp.

Write the equation:

E=QVE = QV

Substitute the values:

E=8.0×4.5E = 8.0 \times 4.5

Calculate:

E=36 JE = 36\text{ J}

The answer is in joules because coulombs multiplied by joules per coulomb gives joules.

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