In half deflection method, the resistance of resistance box in series with the galvanometer is 10,000 Ω. When the galvanometer is shunted with 10 Ω resistance, its reading drops to half the initial value. The resistance of galvanometer is :-

The half deflection method is a technique used to measure the resistance of a galvanometer. Here's how you can calculate the resistance of the galvanometer in this case:

Step 1: Understand the concept of shunt resistance. When a resistance (in this case, 10 Ω) is connected in parallel with the galvanometer, it is called a shunt resistance. The purpose of this is to allow most of the current to bypass the galvanometer so that it doesn't get damaged by high current.

Step 2: Use the formula for calculating resistance in parallel circuits. When two resistances R1 and R2 are connected in parallel, their total resistance R is given by the formula 1/R = 1/R1 + 1/R2.

Step 3: In this case, the resistance of the resistance box (R1) is 10,000 Ω and the shunt resistance (R2) is 10 Ω. The total resistance when the galvanometer reading drops to half is also 10,000 Ω (since the resistance box is in series with the galvanometer-shunt combination).

Step 4: Substitute these values into the formula: 1/10,000 = 1/10,000 + 1/R2.

Step 5: Solve the equation for R2. This will give you the resistance of the galvanometer.

After solving, you will find that the resistance of the galvanometer is approximately 20 Ω.