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  4. In the given potentio-meter circuit, the resistance of uniform cross = section potentiometer wire A B of length 1 m is 10 Ω. When the variable resistance R is 10 Ω, the balance point is obtained for length l as shown. If the variable resistance is doubled, the new balance length is k l. Find k.

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Q. In the given potentio-meter circuit, the resistance of uniform cross = section potentiometer wire $A B$ of length $1 \,m$ is $10\, \Omega$. When the variable resistance $R$ is $10 \,\Omega$, the balance point is obtained for length $l$ as shown. If the variable resistance is doubled, the new balance length is $k l$. Find $k$.Physics Question Image

Current Electricity

Solution:

$V_{A J}=\frac{E}{R+R} \times R_{l}=e$
and $\frac{E}{2 R+R} \cdot R_{l'}=e$
$ \Rightarrow \frac{R_{l'}}{R_{l}}=\frac{l^{\prime}}{l}=\frac{3}{2} $
(since $\left.R \propto l\right)$