Question

A cell of e.m.f 1.5V and negligible internal resistance is connected in series with a potential meter of length 10 m and the total resistance of 20 Ω. What resistance should be introduced in the resistance box such that the potential drop across the potentiometer is one microvolt per cm of the wire?  

Answer 1

Given:

R = 20 Ω, L = 10 m, E = 1.5 V,
K = 1 μV/cm = 1 × (10^-6 /10^-2 ) V/ m
= 10^-4 V/ m 

To find: External resistance (R_E) 

Formula: K = `"V"/"L"`

Calculation: 

Since, I = `"E"/("R" + "R"_"E")`

Also, V = IR = `"ER"/("R" + "R"_"E")`

From formula,

K = `"ER"/(("R" + "R"_"E")"L")`

R + R_E = `"ER"/"KL"`

∴ R_E = `(1.5 xx 20)/(10^-4 xx 10) - 20 = 30000 - 20`

∴ R_E = 29980 Ω 

The external resistance should be 29980 Ω.