Consider a $72 c m$ long wire $A B$ as shown in the figure. The galvanometer jockey is placed at $P$ on $A B$ at a distance $x c m$ from $A$ . The galvanometer shows zero deflection. The value of $x$ , to the nearest integer, is $______$ .

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Solution

Step 1. Given Data,
First unknown resistance $R_{1} = 12 Ω$
Second unknown resistance $R_{2} = 6 Ω$
Length AP $L_{1} = x$
Length PB $L_{2} = 72 - x$
Step 2. The formula used and calculation
Using the galvanometer coil balanced formula,
At balanced conditions,
$\Rightarrow \frac{L_{1}}{R_{1}} = \frac{L_{2}}{R_{2}} \Rightarrow \frac{x}{12} = \frac{72 - x}{6} \Rightarrow \frac{x}{2} = \frac{72 - x}{1} \Rightarrow x = 144 - 2 x \Rightarrow x = \frac{144}{3} \Rightarrow x = 48 c m$
Hence, the value of $x$ , to the nearest integer, is $48 c m$ ,

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Consider a 72cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance xcm from A. The galvanometer shows zero deflection. The value of x, to the nearest integer, is ______.

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