Current Electricity Question 6
Question 6 - 2024 (01 Feb Shift 2)
In a metre-bridge when a resistance in the left gap is $2 \Omega$ and unknown resistance in the right gap, the balance length is found to be $40 \mathrm{~cm}$. On shunting the unknown resistance with $2 \Omega$, the balance length changes by :
(1) $22.5 \mathrm{~cm}$
(2) $20 \mathrm{~cm}$
(3) $62.5 \mathrm{~cm}$
(4) $65 \mathrm{~cm}$
Show Answer
Answer: (1)
Solution:
First case $\frac{2}{40}=\frac{X}{60} \Rightarrow X=3 \Omega$
In second case $X^{\prime}=\frac{2 \times 3}{2+3}=1.2 \Omega$
$\frac{2}{\ell}=\frac{1.2}{100-\ell}$
$200-2 \ell=1.2 \ell$
$\ell=\frac{200}{3.2}=62.5 \mathrm{~cm}$
Balance length changes by $22.5 \mathrm{~cm}$
