A current of \(0.50\,\mathrm{A}\) flows through a resistor for \(2.0\) minutes. Calculate the charge that passes.
\(Q = It = 0.50\times120 = 60\,\mathrm{C}\).
Electricity
10 exam-style questions on current, voltage, resistance, series and parallel circuits, and power. Tap Show answer for full working.
3 Easy4 Medium3 Hard
A \(12\,\mathrm{V}\) battery is connected to a \(4.0\,\Omega\) resistor. Calculate the current.
\(I = V/R = 12/4.0 = 3.0\,\mathrm{A}\).
Calculate the power of a lamp that uses \(60\,\mathrm{J}\) of energy in \(2.0\,\mathrm{s}\).
\(P = E/t = 60/2.0 = 30\,\mathrm{W}\).
Two resistors of \(3.0\,\Omega\) and \(6.0\,\Omega\) are connected in series across a \(9.0\,\mathrm{V}\) supply. Calculate the total resistance and the current in the circuit.
\(R_{\mathrm{tot}} = 9.0\,\Omega\); \(I = 9.0/9.0 = 1.0\,\mathrm{A}\).
The same two resistors (\(3.0\,\Omega\) and \(6.0\,\Omega\)) are connected in parallel across \(9.0\,\mathrm{V}\). Calculate the total resistance and the current through the \(3.0\,\Omega\) resistor.
\(1/R = 1/3 + 1/6 = 1/2 \Rightarrow R = 2.0\,\Omega\).
\(I_{3} = 9.0/3.0 = 3.0\,\mathrm{A}\).
A \(2.0\,\mathrm{kW}\) heater is connected to the \(230\,\mathrm{V}\) mains. Calculate the current it draws and the energy it uses in \(30\) minutes.
\(I = P/V = 2000/230 = 8.7\,\mathrm{A}\).
\(E = Pt = 2000\times1800 = 3.6\times10^{6}\,\mathrm{J}\) (\(3.6\,\mathrm{MJ}\)).
State Ohm’s law. Sketch the current–voltage graph for an ohmic conductor and for a filament lamp.
Ohm’s law: current is proportional to potential difference (at constant temperature); \(V = IR\).
Ohmic: straight line through origin. Filament lamp: curve that flattens (resistance increases as temperature rises).
A wire of length \(2.0\,\mathrm{m}\) and cross-sectional area \(0.50\,\mathrm{mm}^{2}\) has resistance \(0.68\,\Omega\). Calculate its resistivity.
\(\rho = RA/L = 0.68\times0.50\times10^{-6}/2.0 = 1.7\times10^{-7}\,\Omega\,\mathrm{m}\).
In a series circuit the current is the same everywhere. In a parallel circuit the potential difference across each branch is the same. Explain why, in terms of energy and charge.
Series: charge has only one path, so the same charge per second (current) flows through each component. Energy is shared, so PD adds up.
Parallel: each branch is connected directly across the supply, so each experiences the same PD. Charge splits between branches, so currents add.
A fuse is rated at \(3\,\mathrm{A}\). Explain what a fuse does and why a \(13\,\mathrm{A}\) fuse should not be used in a circuit that only needs \(3\,\mathrm{A}\).
A fuse melts (blows) if the current exceeds its rating, breaking the circuit and protecting against overheating/fire.
A \(13\,\mathrm{A}\) fuse would allow a dangerously high current to flow before melting, so the cable or appliance could overheat before the fuse blows.