In the potentiometer circuit shown, the uniform wire AB is supplied separately from battery V. With switch 2 closed and switches 1 and 3 open, the balance length AJ is L₁. With all switches closed, balance length AJ₁ is L₂. Given L₁/L₂ = 3, find n if the internal resistance of the lower battery is r = nR. [See Image.]
Physics · Mixed Chapter
JEE Mains

Question

In the potentiometer circuit shown, the uniform wire AB is supplied separately from battery V. With switch 2 closed and switches 1 and 3 open, the balance length AJ is L₁. With all switches closed, balance length AJ₁ is L₂. Given L₁/L₂ = 3, find n if the internal resistance of the lower battery is r = nR. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — The balance length of the uniform potentiometer wire is proportional to the measured lower-cell terminal voltage, because its own driving-cell potential gradient is unchanged. Thus L₁/L₂ = V₁/V₂ = 3. Step 2 — With only switch 2 closed, the lower cell is connected across three series resistors R. Their load resistance is R₁ = 3R. Hence its terminal voltage is V₁ = ℰ(3R)/(r + 3R). Step 3 — Closing switches 1 and 3 additionally connects alternate junctions, so the three resistors now conn…