Question

In a potentiometer of one metre length, an unknown emf voltage source is balanced at 50 cm length of potentiometer wire while a 6 V battery is balanced at 30 cm length. The emf of unknown voltage source isOptions:Should have chosen

a)10 V

b) 6 V

c) 3 V

d) 9 V

Answer 1

Potential gradient is potential per unit length, which is denoted by $k=\frac{V}{l}or,V=kl$

$6V$ is balanced at $30cmor,\frac{30}{100}m$ , so $6V=k\frac{30}{100}....\left(1\right)$

$XV$ is balanced at $50cmor,\frac{50}{100}m$ , so, $XV=k\frac{50}{100}...\left(2\right)$

Taking ratio of eq(1) and eq(2)

$\frac{6}{X}=\frac{k\frac{30}{100}}{k\frac{50}{100}}$

$\frac{6}{X}=\frac{3}{5}$

$3X=30$

$X=10V$

Hence, he emf of unknown voltage source is:

$X=10V$

.