Question

A millivoltmeter of $25$ millivolt range is to be converted into an ammeter of $25$-ampere range. The value (in ohm) of the necessary shunt will be:

• A. $1$
• B. $0.01$
• C. $0.05$
• D. $0.001$

Answer 1

The correct option is D

$0.001$

Step 1. Given data:

Range of millivoltmeter = $25$ millivolt = $25\times {10}^{-3}$ Volt

The expected range of ammeter $i=25$ ampere

Step 2. Calculating the value of shunt resistance

For making an ammeter, shunt resistance $R_s$ is connected in parallel to the galvanometer.

Here, shunt resistance= $R_s$, $V_g$= galvanometer voltage, $i_g$= full-scale deflection current,

Hence $R_S=\frac{V_g}{\left(i-i_g\right)}..........\left(1\right)$, Where subscript g refers to the galvanometer,

Now $i_g=\frac{V_g}{R_g}=\frac{25\times {10}^{-3}}{R_g}$

Here voltmeter's resistance = $R_g$

Now $R_g\to \infty ,$ Because in an ideal voltmeter, $R\to \infty$

Hence, $i_g\approx 0$

Thus, from $\left(1\right)$,

$R_s=\frac{V_g}{i}=\frac{25\times {10}^{-3}}{25}=0.001\Omega$

Thus, the correct option is option D.