Question

Estimate the resistance of a galvanometer by half-deflection method.

Hint:

The resistance R should be chosen high enough not only to protect the galvanometer from excessive current but also to make the approximation \(G \approx S\) more accurate. A deflection that is large and easily divisible by two (e.g., 30 or 40 divisions) makes the experiment easier and more precise.

Answer 1

Step 1: Understanding the Concept:
The half-deflection method is a technique to determine the resistance of a galvanometer. The main circuit consists of a cell, a high resistance box (R), and the galvanometer (G). A shunt resistance (S) is then connected in parallel with the galvanometer. The value of R is adjusted to get a full-scale or large deflection. Then, S is adjusted until the galvanometer deflection is halved. Under the condition that R is very large, the galvanometer resistance G is approximately equal to the shunt resistance S.
Step 2: Key Formula and Apparatus:
Apparatus Required:
A galvanometer, a battery or cell, two resistance boxes (one of high range, \(\sim 10000 \, \Omega\), and one of low range, \(\sim 200 \, \Omega\)), two one-way keys, and connecting wires.
Key Formula:
The accurate formula for the galvanometer resistance is: \[ G = \frac{R \cdot S}{R - S} \] Where R is the high resistance connected in series, and S is the shunt resistance connected in parallel.
If R is much larger than S (\(R \gg S\)), then \(R - S \approx R\), and the formula simplifies to the approximation: \[ G \approx S \] Step 3: Detailed Procedure:
1. Initial Circuit Setup: Connect the cell, the high resistance box (R), and the galvanometer (G) in series using key \(K_1\).
2. Getting Full Deflection: Take out a high resistance (e.g., 5000 \(\Omega\)) from the resistance box R. Close key \(K_1\) and note the deflection \(\theta\) in the galvanometer. Adjust R such that the deflection is large and is an even number of divisions (e.g., 30 divisions).
3. Applying Shunt: Connect the low resistance box (S) in parallel with the galvanometer through a second key \(K_2\).
4. Getting Half Deflection: Close key \(K_2\). Adjust the value of S from the resistance box until the deflection in the galvanometer becomes exactly half of the initial deflection, i.e., \(\theta/2\).
5. Recording Values: Record the values of R and S. Repeat the experiment for different values of R and find the corresponding S.
Step 4: Calculation:
For each set of readings, calculate the galvanometer resistance G using the formula \( G = \frac{R \cdot S}{R - S} \).
Find the mean of the calculated values of G. \[ G_{mean} = \frac{G_1 + G_2 + G_3}{3} \] The mean value is the resistance of the given galvanometer.