Question

A potential difference of $240V$ is maintained across a $12000$ ohm rehostat and voltmeter V has resistance of $3000$ ohm and point $C$ is at the centre of $A$ and $B$ as shown in figure. What is the reading in voltmeter?

Answer 1

In case of linear rheostat

$R\alpha L$ (length)

$\frac{R_{EC}}{R_{ED}}=\frac{EC}{ED}$

$EC=\frac{1}{2}ED$

As the resistance $R_{EC}(=6000\Omega )$ is in parallel to resistance of $3000\Omega$ (Voltmeter). So the effective resistance b/w point $E$ and $C$ will be

$R_{EC}=\frac{3000\times 6000}{3000+6000}=2000\Omega$

Resistance between point $DC$ is $6000\Omega$ $R_{DC0}$ and $R_{EC}$ are in series so voltmeter reading will be

$V_{AC}=\frac{R_{EC}^{\prime }}{R_{DC}+R_{EC}^{\prime }}\times V_{AB}$

$=\frac{2000}{48000}\times 240=60Volt$