Question

A potentiometer wire of length 20 m has a resistance of 50 ohms. It is connected in series with a resistance box and a 5 V storage cell. If the potential gradient along the wire is 0.5 mV/cm, what is the resistance unplugged in the box?

(a) 450 ohms

(b) 400 ohms

(c) 405 ohms

(d) 500 ohms

The question was asked by my school principal while I was bunking the class.

The origin of the question is Current Electricity in section Current Electricity of Physics – Class 12

Answer 1

Correct option is (a) 450 ohms

To elaborate: Potential gradient along the potentiometer wire = \(\frac {potential \, difference \, along \, wire}{length \, of \, wire}\).

0.5 × 10^-3 = I × \(\frac {50}{1000}\)

I = 0.5 × 10^-3 × \(\frac {1000}{50}\)

I = \(\frac {1}{100}\)

So, \(\frac {5}{(50 + R)} = \frac {1}{100}\)

R + 50 = 500

R = 450 ohms

Therefore, the resistance unplugged in the box is 450 ohms.