In a meter bridge experiment null point is obtained at 20 cm from one end when resistance X is balanced against resistance Y, where X < Y. Then, the new position of the null point from the same end if X is replaced by 4X will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 50 cm
At the null point the meter bridge (a Wheatstone bridge) is balanced, so the ratio of the resistances equals the ratio of the wire lengths on the two sides: \( X/Y = l/(100-l) \).
First balance, \( l = 20\,\mathrm{cm} \):
\( \displaystyle \frac{X}{Y} = \frac{20}{100-20} = \frac{1}{4} \)
Now X is replaced by 4X, so the ratio becomes four times larger:
\( \displaystyle \frac{4X}{Y} = 4\times\frac{1}{4} = 1 = \frac{l'}{100-l'} \)
\( l' = 100-l' \Rightarrow l' = 50\,\mathrm{cm} \)