Question

To know the resistance $G$ of a galvanometer by half deflection method, a battery of emf $V_E$ and resistance $R$ is used to deflect the galvanometer by angle $\theta$. If a shunt of resistance $S$ is needed to get half deflection then $G, R$ and $S$ are related by the equation :

• A. $2S (R+G)=RG$
• B. $S (R+G)=RG$
• C. $2S=G$
• D. $2G=S$

Answer 1

The Correct Option is B

To solve this problem, we will use the concept of the 'Half Deflection Method', which is commonly used to determine the resistance of a galvanometer. Let's understand the step-by-step reasoning involved in finding the relationship between the given quantities: resistance of the galvanometer \(G\), resistance across battery \(R\), and shunt resistance \(S\).

1. In the half deflection method, initially, when no shunt is connected, the current \(I\) passes through the galvanometer and the deflection is \(\theta\). The condition here is: \(I = \frac{V_E}{R + G}\)
2. The galvanometer constant \(k\) relates current and deflection: \(I = k \times \theta\)
3. When shunt \(S\) is connected, the deflection becomes half. Thus, the effective current through the galvanometer becomes \(\frac{I}{2}\) since the deflection is half. \(\frac{I}{2} = \frac{V_E}{R + \frac{GS}{G + S}}\)
4. The above scenario can be simplified as: \(\frac{I}{2} = k \times \frac{\theta}{2}\)
5. Substitute the expression for \(I\): \(\frac{k \theta}{2} = \frac{V_E \times G}{R \times (G + S) + G \times S}\)
6. The equation simplifies and results in: \(S(R + G) = RG\)

The correct option, as derived through the steps above, is \(S(R + G) = RG\). This is consistent with the nature of the half deflection method where the current through the galvanometer is halved by introducing a shunt resistance \(S\).

Thus, the correct answer is \(S(R + G) = RG\), which matches the provided correct answer option.