Question

In a potentiometer experiment, the balancing length of a cell is $560\, cm$. When an external resistance of $10 \, \Omega$ is connected in parallel to the cell, the balancing length changes by $60 \,cm$.The internal resistance of a cell is

• A. $1.4\, \Omega$
• B. $1.6\, \Omega$
• C. $0.12 \, \Omega$
• D. $1.2\, \Omega$

Answer 1

Answer: (D)

Consider a cell ofe mf E and balancing length$l_1$
$E = kl_1$
The potential difference is balanced by length $l_2$.
$V = kl_2$
The internal resistance of the cell is given by
$r = \left(\frac{E-V}{V}\right)R =\left(\frac{E}{V } - 1\right)R = \left(\frac{l_{1}}{l_{2}} - 1\right)R $
$ = \left(\frac{560}{560 - 60} - 1 \right) 10 = \left(\frac{56}{50} - 1 \right)10 $
$ = \frac{6}{5} = 1.2 \Omega$