Example Question

A resistor is connected to a power supply so that the potential difference across it is 6.0 V. The current through it is 0.25 A, and the supply is switched on for 2.0 minutes.Calculate:(i) the resistance of the resistor(ii) the charge that flows through it(iii) the energy transferred in the resistor(iv) the number of electrons that pass through it.(i) Resistance is the ratio of p.d. to current:R = V ÷ I = 6.0 ÷ 0.25 = 24 Ω(ii) Current is the rate of flow of charge, so ΔQ = IΔt. First convert the time to seconds: 2.0 minutes = 120 s.ΔQ = 0.25 × 120 = 30 C(iii) Potential difference is the energy transferred per unit charge, V = W/Q, so W = QV:W = 30 × 6.0 = 180 J(iv) Each electron carries a charge of magnitude e = 1.6 × 10^-19 C, so the number of electrons is:N = Q ÷ e = 30 ÷ (1.6 × 10^-19) = 1.9 × 10²⁰Check the units at each step: Ω = V A^-1, C = A s and J = C V. Forgetting to convert minutes to seconds is the most common mistake in questions like this, and it would make answers (ii), (iii) and (iv) all 60 times too small.