Question

Two different voltmeters are used to measure the voltage across resistor $R_B$ in the circuit shown below.

The meters are as follows.

$MeterA:S=1k\Omega /V,R_m=0.2k\Omega ,range=10V$

$MeterB:S=20k\Omega /V,R_m=1.5k\Omega ,range=10V$

Voltage across $R_B$ when meter A, meter B are used respectively

• A. 3.53 V, 4.9 V
• B. 4.9 V, 3.53 V
• C. 3.53, V 4.2 V
• D. 3.2 V, 4.9 V

Answer 1

The correct option is A 3.53 V, 4.9 V

Resistance of meter,
$A=1k\Omega /V\times 10V$
$=10k\Omega$

The parallel combination of $R_B$ and meter A is

$R_{e1}=\frac{5\times 10}{5+10}=3.33k\Omega$

$\therefore V_{RB}=30\times \frac{3.33}{3.33+25}=3.53V$

Resistance of meter B,

$=20k\Omega /V\times 10$

$=200k\Omega$

The parallel combination of $R_B$ and meter B is

$=\frac{5\times 200}{5+200}=4.88k\Omega$

$\therefore V_{RB}=30\times \frac{4.88}{4.88+25}=4.9V$