Question

A potential difference of $220\, V$ is maintained across a 12000 ohm rheostat $A B$ as shown in figure. The voltmeter $V$ has a resistance of $6000\, ohm$ and point $C$ is at one fourth of the distance from $A$ to $B$. What is the reading in the voltmeter ?

• A. 32 V
• B. 36 V
• C. 40 V
• D. 42 V

Answer 1

Answer: (C)

As in case of linear rheostat, $R \propto$ length $(L)$
$\frac{R_{A C}}{R_{A B}}=\frac{A C}{A B}$
Here, $R_{A B}=12000\, \Omega$ and $A C=\frac{1}{4} A B$
$\therefore R_{A C}=12000 \times \frac{1}{4}=3000\, \Omega$
As the resistance $R_{A C}(=3000\, \Omega)$ is in parallel with voltmeter of resistance of $6000\, \Omega$.
Therefore, the effective resistance between points $A$ and $C$ will be
$R_{A C}'=\frac{3000 \times 6000}{(3000+6000)}=2000\, \Omega$
Resistance between points $B$ and $C$
$R_{B C}=R_{A B}-R_{A C}=12000\, \Omega-3000\, \Omega=9000\, \Omega$
$R_{B C}$ and $R_{A C}'$ are in series.
Therefore, the voltmeter reading will be
$V_{A C}=\frac{R_{A C}' V_{A B}}{\left(R_{B C}+R_{A C}'\right)}$
$=\frac{2000}{(9000+2000)} \times 220=40\, V$