Physics 9702 · AS & A Level · Potential dividers

Potential dividers — practice question

Figure 6.1 shows a network containing three resistors with resistances $R_1$, $R_2$ and $R_3$. The potential difference across each resistor is $V_1$, $V_2$ and $V_3$ respectively. The current through the resistor combination is $I$, and the overall potential difference across the combination is $V$.
(a)[2]

Show that the equivalent resistance $R$ for the network is $R = R_1 + R_2 + R_3$.

(b)

A battery with electromotive force (e.m.f.) $8.0\,\text{V}$ and negligible internal resistance is connected to a thermistor, a switch X and two fixed resistors, as shown in Fig. 6.2. The resistance of resistor $R_1$ is $6.0\,\text{k}\Omega$ and that of resistor $R_2$ is $4.0\,\text{k}\Omega$.

(b(i))[2]

The switch X is open. Calculate the potential difference across $R_1$.

(b(ii))[2]

Switch X is now closed. The thermistor has resistance $12.0\,\text{k}\Omega$. Calculate the current in the battery.

(c)[3]

In the circuit in (b), switch X stays closed. The thermistor’s temperature falls. Referring to the current in the battery, state and explain the effect, if any, of the temperature decrease on the power produced by the battery.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: States $V = V_1 + V_2 + V_3$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI