Understanding Galvanometer Multiplying Factor

This question asks us to find the multiplying factor of a galvanometer when it's converted into an ammeter using a shunt resistor. The multiplying factor tells us how many times the current in the main circuit is greater than the current passing through the galvanometer coil.

Key Components and Formula

We are given the following information:

• Galvanometer internal resistance ($R_g$) = 100 ohm
• Shunt resistance ($R_s$) = 20 ohm

The formula to calculate the multiplying factor (MF) when a galvanometer is shunted is:

$$ \text{MF} = 1 + \frac{R_g}{R_s} $$

Where:

• $R_g$ is the resistance of the galvanometer coil.
• $R_s$ is the resistance of the parallel shunt resistor.

Step-by-Step Calculation

Now, let's substitute the given values into the formula:

1. Identify the values: $R_g = 100 \text{ ohm}$ and $R_s = 20 \text{ ohm}$.
2. Calculate the ratio $\frac{R_g}{R_s}$: $$ \frac{R_g}{R_s} = \frac{100 \text{ ohm}}{20 \text{ ohm}} = 5 $$
3. Add 1 to the ratio to find the multiplying factor: $$ \text{MF} = 1 + 5 = 6 $$

Therefore, the multiplying factor for this galvanometer setup is 6.

Conclusion

The calculation shows that the multiplying factor is 6. This means the ammeter, formed by shunting the galvanometer, can measure currents 6 times larger than the maximum current the galvanometer coil itself could handle without the shunt.