DC Circuits — practice questions

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.