To send 10% of the main current through a moving coil galvanometer of resistance 99 ohm the shunt required is a) 10 ohm b) 9.9 ohm c) 9 ohm d) 11 ohm

To determine the shunt resistance required to send 10% of the main current through a moving coil galvanometer with a resistance of 99 ohms, we can use the formula for calculating shunt resistance in parallel circuits. Let's break this down step by step.

Understanding the Circuit Configuration

A moving coil galvanometer measures current by deflection of a coil in a magnetic field. In this case, we want only 10% of the total current to pass through the galvanometer. The rest will pass through a shunt resistor connected in parallel. This shunt allows us to protect the galvanometer from excessive current, ensuring accurate readings.

The Formula for Shunt Resistance

The shunt resistance (R_s) can be calculated using the formula:

• R_s = (R_g * I_g) / (I - I_g)

Where:

• R_g = Resistance of the galvanometer (99 ohms)
• I_g = Current through the galvanometer (10% of total current, I)
• I = Total current

Setting Up the Calculation

Let’s denote the total current as I. That means:

• I_g = 0.1I (10% of total current)
• I - I_g = 0.9I (the current through the shunt)

Substituting these into our shunt resistance formula gives:

• R_s = (R_g * 0.1I) / (0.9I)

The current I cancels out, simplifying our equation to:

• R_s = (R_g * 0.1) / 0.9

Plugging in the Values

Now, we substitute R_g with 99 ohms:

• R_s = (99 * 0.1) / 0.9
• R_s = 9.9 / 0.9
• R_s = 11 ohms

Conclusion on Shunt Resistance

Therefore, the required shunt resistance is 11 ohms. This means that to allow only 10% of the total current to pass through the galvanometer while the rest flows through the shunt, you would need a shunt resistor of 11 ohms. So the correct answer from the options provided is d) 11 ohm.