E.m.f. and p.d: (d) energy transfer; W = VQ ; W = EQ .

The idea

The equations W = VQ and W = EQ give the energy transferred when charge moves through a potential difference or an electromotive force. W is the energy transferred in joules, V is the p.d. in volts, E is the e.m.f. in volts and Q is the charge in coulombs. For example, if 5 C of charge passes through a p.d. of 12 V, the energy transferred is W = 12 V × 5 C = 60 J. Because 1 V = 1 J C⁻¹, the product of volts and coulombs is joules. The two equations have the same form because both e.m.f. and p.d. are energy per unit charge; the symbol used indicates whether the energy is supplied by a source or transferred by a component.

What earns the marks

• W = VQ gives the energy transferred when charge Q passes through a potential difference V.
• W = EQ gives the energy transferred when charge Q passes through an electromotive force E.
• In both equations W is in joules, Q is in coulombs, and V or E is in volts.
• The equations work because 1 V = 1 J C⁻¹, so multiplying volts by coulombs gives joules.
• The same relationship applies to e.m.f. and p.d. because both are energy per unit charge; the symbol used shows whether energy is supplied or transferred away.

Common mistakes and how to put them right

• Using the wrong unit for charge.

  Put it right: Q must be in coulombs, so convert millicoulombs or microcoulombs before substituting.

• Mixing up V and E in the two forms.

  Put it right: Use V for a p.d. across a component and E for the e.m.f. of a source.

• Forgetting that the product VQ has units of joules.

  Put it right: Check by substituting 1 V = 1 J C⁻¹ so that V × C = J.

Exam tips

• Write down the equation, substitute values with units, and state the answer in joules.
• If charge is given in millicoulombs or microcoulombs, convert to coulombs before multiplying.
• Use W = VQ for energy transferred by a component and W = EQ for energy supplied by a source, and label the symbol accordingly.