Physics - Current Electricity Question with Solution | TestHub

Total resistance of the circuit is $R_{total}=R_w+R_s=20+15=35\Omega$.

Current in the circuit is $I=\frac{E}{R_{total}}=\frac{6}{35}\text{A}$.

Potential difference across the potentiometer wire is $V_w=I{R}_w=\frac{6}{35}\times 20=\frac{24}{7}\text{V}$.

Length of the potentiometer wire is $L=400\text{cm}=4\text{m}$.

Potential gradient is $k=\frac{V_w}{L}=\frac{\frac{24}{7}}{4}=\frac{6}{7}\text{V/m}$.

Given $k=\frac{x}{7}\text{V/m}$, comparing the two expressions yields $x=6$.

Answer: $6$