A current of 2 A flows in the system of conductors as shown in the figure. The potential difference VP - VR will be:
Answer & explanation
Correct answer: option 2
Resistance between Q and S,
$R'=\frac{5 \times 10}{5+10}=\frac{10}{3} \Omega$
Potential difference across Q and S,
$V_{Q}-V_{S}=\frac{2 \times 10}{3}=\frac{20}{3} V$
Current through arm QPS, $I_1=\frac{20}{3 \times 5}=\frac{4}{3} A$
$V_{Q}-V_{P}=\frac{4}{3} \times 2=\frac{8}{3} V$
Current through arm QRS, $I_2=\frac{20 / 3}{10}=\frac{2}{3} A$
$V_{Q}-V_{R}=\frac{2}{3} \times 3=2 V$
From equations (i) and (ii),
$V_P-V_R=\left(V_Q-V_R\right)-\left(V_Q-V_P\right)$
$=2-\frac{8}{3}=\frac{-2}{3} \approx-1 V$