Question

A certain unknown resistance is connected in the left gap and a resistance box in the right gap of a metre bridge. By introducing a resistance of 10 W with the help of resistance box, the balance point is determined. If the balance point shift by 20 cm on increasing the resistance from the resistance box by 12.5 W ,then value of unknown resistance is –

• A. 15 W
• B. 25 W
• C. 10 W
• D. 20 W

Answer 1

Answer: (A)

15 W

Answer 2

Let unknown resistance be X. In first case, if l is the balancing length then, = $\frac { \ell } { ( 100 - \ell ) }$

X = $\frac { 10 \ell } { ( 100 - \ell ) }$ …………..(i)

In second case, R = 10 + 12.5 = 22.5 W and

l ' = l – 20

\ = $\frac { \ell ^ { \prime } } { \left( 100 - \ell ^ { \prime } \right) }$ or $\frac { \mathrm { X } } { 22.5 }$ = $\frac { \ell - 20 } { 100 - ( \ell - 20 ) }$

or X = $\frac { 22.5 ( \ell - 20 ) } { 120 - \ell }$ ……….(ii)

Solving eqs (i) and (ii) we get

l = 60 cm and X = 15W