JEE Main 2024 — Current Electricity Question with Solution

To determine the value of the shunt resistor required to convert the galvanometer into an ammeter capable of measuring a current of $$8\mathrm{A}$$, we need to use the concept of shunting where the additional resistor (shunt) is placed in parallel with the galvanometer.

The formula for calculating the value of the shunt resistor $R_s$ is given by:

$$R_s=\frac{R_g\cdot I_g}{I-I_g}$$

Where:

$R_g$ = resistance of the galvanometer = $$10\Omega$$

$I_g$ = full-scale deflection current of the galvanometer = $$3\mathrm{mA}$$ = $$0.003\mathrm{A}$$

$I$ = total current to be measured = $$8\mathrm{A}$$

Substituting these values into the formula:

$$R_s=\frac{10\Omega \cdot 0.003\mathrm{A}}{8\mathrm{A}-0.003\mathrm{A}}$$

Perform the calculations:

$$R_s=\frac{0.03\Omega \cdot \mathrm{A}}{7.997\mathrm{A}}$$

$$R_s\approx 3.75\times 10^{-3}\Omega$$

Thus, the value of the shunt resistor should be:

Option A: $$3.75\times 10^{-3}\Omega$$