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  4. A potentiometer wire AB is 100 cm long and has a total resistance of 10 ohm. If the galvanometer shows zero deflection at the position C, then find the value of unknown resistance R. (in Ω )

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Q. A potentiometer wire $AB$ is $100\, cm$ long and has a total resistance of $10\, ohm$. If the galvanometer shows zero deflection at the position $C$, then find the value of unknown resistance $R$. (in $\Omega$ )Physics Question Image

Current Electricity

Solution:

Potential gradient
$x=$ current $\times$ Resistance per unit length
$x=\frac{10\, V}{10\, \Omega} \times \frac{10}{100}$
$x=0.1\, V / cm$
Potential difference across $R$ is balanced at $40\, cm$.
$\therefore V=x \times 40$
$V=0.1 \times 40=4$ volt.
But $V=I \times R$
$4=\left(\frac{5}{R+1}\right) R$
$\Rightarrow 4 R+4=5 R$
$\Rightarrow R=4\, \Omega$