Electricity & Electromagnetism — practice questions

Two parallel plates are $5.0$ mm apart with a potential difference of $150$ V across them.

Calculate the electric field strength between them.

Two parallel plates $8.0$ mm apart are connected to a $240$ V supply.

Calculate the field strength between them. The plates are then moved to a separation of $12$ mm with the same supply. Calculate the new field strength and explain why it has changed.

A student sets up two parallel plates connected to a variable power supply, and places a small charged sphere in the gap. They observe that moving the sphere to different positions between the plates does not change the force on it, but moving one plate further away does.

Explain fully why the field between parallel plates is uniform, why the position of the sphere makes no difference, and what would happen to the force if the charge on the sphere were doubled while the plates were unchanged.

A charge of $5.0$ µC is placed in a uniform electric field of strength $2.0 \times 10^4$ N C⁻¹.

Calculate the force on the charge.

A charge of $4.0$ µC is placed between two parallel plates $2.0$ mm apart with $100$ V across them.

Calculate the force on the charge. State and explain the direction of the force if the charge is negative.

A tiny charged oil drop of mass $3.2 \times 10^{-15}$ kg is held stationary between two horizontal parallel plates $6.0$ mm apart connected to a $400$ V supply.

Calculate the charge on the drop, and determine how many excess electrons it carries (electron charge $= 1.6 \times 10^{-19}$ C). Explain fully why the drop must be negatively charged if the upper plate is positive, and explain what would happen if the voltage were then doubled.

A charge of $3.0$ µC moves through a potential difference of $200$ V.

Calculate the energy transferred.

Two parallel plates $5.0$ mm apart have a field strength of $3.0 \times 10^4$ N C⁻¹ between them. A $6.0$ nC charge is moved $3.0$ mm from the positive plate toward the negative plate, and then $4.0$ mm parallel to the plates.

Calculate the total work done on the charge, and explain why the second movement contributes nothing.

Two horizontal parallel plates are $10$ mm apart with $500$ V across them, the lower plate being positive. A proton (charge $+1.6 \times 10^{-19}$ C, mass $1.67 \times 10^{-27}$ kg) is released from rest at the lower plate.

Calculate the energy transferred to the proton and the speed at which it reaches the upper plate. Explain fully what energy changes occur, and explain why the answer would be unchanged if the proton took a longer, curved path between the plates.

A proton (charge $1.6 \times 10^{-19}$ C) is accelerated from rest through a potential difference of $1000$ V.

Calculate the kinetic energy it gains.

An electron (charge $1.6 \times 10^{-19}$ C, mass $9.11 \times 10^{-31}$ kg) is accelerated from rest through a potential difference of $800$ V.

Calculate its final speed, and explain the energy change that takes place.

In an oscilloscope, an electron beam is first accelerated from rest through $2500$ V, then passes horizontally between two deflection plates $50$ mm long which are $10$ mm apart with $80$ V across them.

Calculate the speed of the electrons entering the deflection plates, and their vertical deflection on leaving them. Explain fully why the deflection would be reduced if the accelerating voltage were increased, and identify the assumption you have made about gravity.

A charge of $45$ C flows past a point in a circuit in $15$ s.

Calculate the current.

A current of $500$ mA flows through a resistor for $4.0$ minutes, and the resistor has a potential difference of $6.0$ V across it.

Calculate the charge that flows and the energy transferred in the resistor. Explain what the $6.0$ V tells you about each coulomb of charge.

A student says: "In a series circuit with a battery and two identical bulbs, the first bulb uses up some of the current, so the second bulb is dimmer. The current comes out of the battery and gets used up as it goes round."

Discuss this statement fully. Explain what is actually conserved, what is actually used up, and what the student would observe.

A resistor has a potential difference of $9.0$ V across it and a current of $0.30$ A through it.

Calculate its resistance.

A student plots a $V$–$I$ graph for a metal wire held at constant temperature and finds a straight line through the origin. They then repeat it for a filament lamp and obtain a curve.

Explain what each graph shows about the resistance of the component, and explain the shape of the lamp's graph.

A filament lamp's $V$–$I$ graph passes through $(0.10\text{ A}, 0.30\text{ V})$ and $(0.50\text{ A}, 6.0\text{ V})$.

Calculate the resistance at each point. Explain fully why using the gradient between the two points would give a meaningless answer, and explain, in terms of the behaviour of electrons and ions, why the resistance changes as it does. Comment on what this implies about a lamp at the instant it is switched on.

A lamp operates at $12$ V and draws a current of $2.5$ A.

Calculate its power.

A $2.0$ kW jug is connected to a $230$ V supply and runs for $3.0$ minutes.

Calculate the current it draws and the energy it transfers, and state the main energy transformation taking place.

Electricity is transmitted from a power station to a town along cables of total resistance $4.0$ Ω. The station delivers $2.0$ MW of power. Compare transmitting it at $10$ kV with transmitting it at $200$ kV.

Calculate the current and the power wasted in the cables in each case, and explain fully why high voltages are used for transmission, and what the trade-off is.

Two resistors of $15$ Ω and $25$ Ω are connected in series.

Calculate the total resistance.

A $24$ V supply is connected in series with a $30$ Ω and a $50$ Ω resistor.

Calculate the current in the circuit and the voltage across each resistor. Explain why the current is the same through both.

Two identical lamps are connected in series to a $12$ V battery, and both glow at normal brightness. A third identical lamp is then added in series with the other two.

Explain fully what happens to the current, the voltage across each lamp, and the brightness, giving quantitative reasoning. Each lamp may be treated as a fixed $6.0$ Ω resistance.

Two $20$ Ω resistors are connected in parallel.

Calculate the total resistance.

A $12$ V supply is connected across a $40$ Ω resistor and a $60$ Ω resistor in parallel.

Calculate the total resistance and the current in each branch. Explain why the total resistance is less than either individual resistance.

A house is wired so that all its appliances are in parallel across the $230$ V mains. A $2.0$ kW jug, a $100$ W lamp and a $1.5$ kW heater are all switched on.

Calculate the current drawn by each and the total current. Explain fully why household wiring uses parallel rather than series connection, and explain what determines the fuse rating needed for the circuit.

A $10$ Ω resistor is connected in series with a parallel combination of two $20$ Ω resistors.

Calculate the total resistance of the circuit.

A $18$ V supply is connected in series with a $6.0$ Ω resistor and a parallel combination of a $20$ Ω and a $30$ Ω resistor.

Calculate the total current and the current in the $20$ Ω branch. Explain why the full supply voltage is not across the parallel group.

A $24$ V supply is connected in series with a $5.0$ Ω resistor and a parallel combination of two identical $20$ Ω lamps. A third identical $20$ Ω lamp is then connected in parallel with the other two.

Calculate the current through one lamp before and after the third is added, and explain fully why the two original lamps become dimmer even though nothing about them was changed.

A wire of length $0.15$ m carries a current of $4.0$ A at right angles to a magnetic field of $0.20$ T.

Calculate the force on the wire.

A straight wire carrying a current of $6.0$ A lies in a magnetic field of $0.30$ T. The length of wire in the field is $5.0$ cm.

Calculate the force on the wire when the current is perpendicular to the field. State and explain what the force would be if the wire were rotated so that the current ran parallel to the field.

A simple DC motor consists of a rectangular coil of $50$ turns, each of length $6.0$ cm along the sides that lie in the field, carrying a current of $1.2$ A in a magnetic field of $0.40$ T.

Calculate the force on one side of the coil. Explain fully why the coil rotates rather than moving in a straight line, and explain the purpose of the split-ring commutator and what would happen without it.

A charge of $3.2 \times 10^{-19}$ C moves at $5.0 \times 10^5$ m s⁻¹ perpendicular to a magnetic field of $0.40$ T.

Calculate the force on the charge.

An electron enters a uniform magnetic field at right angles to the field lines and follows a circular path.

Explain why the path is circular, and explain why the electron's speed does not change while it is in the field.

An electron and a proton, both travelling at $3.0 \times 10^6$ m s⁻¹, enter the same uniform magnetic field of $0.25$ T at right angles to the field, moving in the same direction.

Calculate the radius of each particle's circular path. Explain fully why they curve in opposite directions, and compare what would happen if they instead entered a uniform electric field.

A conductor $0.40$ m long moves at $2.5$ m s⁻¹ perpendicular to a magnetic field of $0.30$ T.

Calculate the voltage induced across the conductor.

A metal rod is moved at a steady speed across a uniform magnetic field, and a voltage is measured across its ends.

Explain how this voltage is produced. State two changes that would increase it, and state what happens if the rod is instead moved parallel to the field lines.

A student moves a conducting rod across a magnetic field, first with the rod's ends unconnected, then with the ends connected by a wire to form a complete circuit. They notice that the rod is noticeably harder to push in the second case.

Explain fully why a voltage is induced, why a current flows only in the second case, and why the rod becomes harder to push. Refer to energy conservation in your answer.