Electrical Systems — practice questions

A cell of emf $9.0$ V has an internal resistance of $1.5$ Ω and supplies a current of $2.0$ A.

Calculate the terminal voltage of the cell.

A cell of emf $6.0$ V and internal resistance $0.80$ Ω is connected to a $2.2$ Ω resistor.

Calculate the current and the terminal voltage. Explain why the terminal voltage is less than the emf.

A car battery has an emf of $12.6$ V and an internal resistance of $0.020$ Ω. The headlights draw $10$ A. When the starter motor is engaged it draws an additional $200$ A.

Calculate the terminal voltage in each case, and explain fully why the headlights dim when the engine is started. Discuss why a battery in poor condition makes this effect much worse.

At a junction in a circuit, currents of $2.0$ A and $3.5$ A flow in, and two currents flow out. One of the outgoing currents is $1.5$ A.

Calculate the other outgoing current, and state which law you used.

State Kirchhoff's two laws, and explain what conservation principle each one expresses.

A $9.0$ V battery of internal resistance $0.50$ Ω and a $6.0$ V battery of internal resistance $0.30$ Ω are connected in parallel (positive to positive) across a $3.0$ Ω resistor.

Use Kirchhoff's laws to find the current in each branch. Interpret the sign of each result physically, and explain why connecting batteries of different emf in parallel is generally inadvisable.

A $100$ µF capacitor is charged to $9.0$ V.

Calculate the charge stored.

A parallel plate capacitor has plates of area $0.020$ m² separated by $1.0$ mm of air.

Calculate its capacitance. Then state and explain what happens to the capacitance if the plate separation is halved.

A parallel plate capacitor is charged by a battery to $12$ V and then disconnected from the battery. A dielectric slab of relative permittivity $4.0$ is then slid between the plates.

Explain fully what happens to the charge, the capacitance, the voltage and the stored energy. Then explain how the answers would differ if the capacitor had been left connected to the battery throughout.

Capacitors of $4.0$ µF and $6.0$ µF are connected in parallel.

Calculate the total capacitance.

Capacitors of $12$ µF and $4.0$ µF are connected in series across a $20$ V supply.

Calculate the total capacitance and the voltage across each capacitor. Explain why the smaller capacitor has the larger voltage across it.

An engineer has three identical $10$ µF capacitors, each rated at a maximum of $16$ V. They need a combination that can safely withstand $40$ V.

Determine an arrangement that meets this requirement and calculate its capacitance and the energy it stores at $40$ V. Explain why the series arrangement raises the voltage rating, and discuss the trade-off involved.

A $50$ µF capacitor is charged through a $20$ kΩ resistor.

Calculate the time constant of the circuit.

A $10$ µF capacitor is charged through a $100$ kΩ resistor from a $12$ V supply.

Calculate the time constant and the initial current. Explain why the current decreases as the capacitor charges.

A camera flash uses a $470$ µF capacitor charged to $300$ V. The capacitor is charged through a $150$ kΩ resistor, and discharges through the flash tube, which has a resistance of about $2.0$ Ω.

Calculate the energy stored, the charging time constant and the discharging time constant. Explain fully why this arrangement produces a very bright but very brief flash, and why the photographer must wait between shots.

A single loop of area $0.025$ m² lies perpendicular to a magnetic field of $0.40$ T.

Calculate the magnetic flux through the loop.

A coil of $400$ turns and area $2.5 \times 10^{-3}$ m² is in a magnetic field that falls uniformly from $0.80$ T to zero in $0.020$ s.

Calculate the induced emf, and explain why no emf would be induced if the field were held steady at $0.80$ T.

A strong bar magnet is dropped down a long vertical copper tube. It is observed to fall much more slowly than an identical unmagnetised bar dropped down the same tube, eventually reaching a constant slow speed.

Explain fully why this happens, referring to Faraday's law, Lenz's law and conservation of energy. Explain also why the magnet reaches a constant speed rather than continuing to slow down.

A coil of inductance $0.50$ H carries a current changing at $8.0$ A s⁻¹.

Calculate the magnitude of the back emf induced.

A $0.20$ H inductor is connected in series with a $50$ Ω resistor across a $10$ V supply.

Calculate the time constant and the final steady current. Explain why the current does not reach its final value immediately.

A relay coil of inductance $0.80$ H and resistance $40$ Ω is operated from a $24$ V supply. When the switch is opened, the current falls to zero in about $0.50$ ms and a bright spark jumps across the switch contacts.

Calculate the steady current, the energy stored, and the emf generated as the current collapses. Explain fully why the spark occurs, and explain how a diode connected across the coil prevents it.

A transformer has $500$ turns on the primary and $2500$ turns on the secondary. The primary voltage is $12$ V.

Calculate the secondary voltage and state whether this is a step-up or step-down transformer.

A transformer steps $230$ V down to $9.0$ V and is connected to a device drawing $1.5$ A. Assume it is ideal.

Calculate the primary current, and explain why a transformer will not work if connected to a DC supply.

A power station generates $50$ MW at $25$ kV. It is transmitted $150$ km along cables of total resistance $8.0$ Ω, first stepping the voltage up to $220$ kV and stepping it back down at the far end.

Calculate the transmission current and power loss with and without the step-up transformer. Explain fully why transformers make the grid viable, and explain why real transformers are built with laminated cores.

An alternating supply has a peak voltage of $40$ V.

Calculate its rms voltage.

A $12$ V rms AC supply is connected across a $48$ Ω resistor.

Calculate the peak voltage, the rms current and the average power dissipated. Explain why rms values, rather than peak values, are used for power calculations.

A student connects a $100$ Ω resistor first to a $24$ V DC supply, then to an AC supply whose oscilloscope trace shows a peak-to-peak voltage of $68$ V. They claim the AC supply must deliver more power because its trace reaches a higher voltage than $24$ V.

Calculate the average power in each case and evaluate the student's claim. Explain fully what the rms value represents and why the sine wave's average power is exactly half its peak power.

A $0.10$ H inductor is connected to a $50$ Hz supply.

Calculate its inductive reactance.

A $40$ Ω resistor is in series with a capacitor of reactance $30$ Ω across an AC supply.

Calculate the impedance of the circuit, and explain why the resistance and the reactance cannot simply be added together.

A series circuit contains a $50$ Ω resistor, a $0.20$ H inductor and a $20$ µF capacitor, connected to a $12$ V rms supply.

Calculate the impedance and the current at $50$ Hz and at $200$ Hz. Draw on phasor reasoning to explain how the circuit's behaviour changes between the two frequencies, and predict what would happen at a frequency between them.

A series LCR circuit has $L = 0.10$ H and $C = 10$ µF.

Calculate its resonant frequency.

A series LCR circuit contains a $25$ Ω resistor and is connected to a $10$ V rms supply.

State the impedance and current at resonance, and explain why the impedance is a minimum at that frequency.

A radio tuning circuit consists of a $2.0$ mH inductor, a variable capacitor and a $12$ Ω resistance, receiving signals of $1.0$ V rms.

Calculate the capacitance needed to tune to a station broadcasting at $800$ kHz, and the current at resonance. Explain fully how the circuit selects one station out of many, and discuss why a lower resistance improves the receiver.