A teacher in his physics laboratory allotted an experiment to determine the resistance (G) a galvanometer. Students took the observations for `1/3` deflection in the galvanometer. Which of the below is true for measuring value of G?

Options

A. `1/3` deflection method cannot be used for determining the resistance of the galvanometer.
B. `1/3` deflection method can be used and in this case the G equals to twice the value of shunt resistance(s).
C. `1/3` deflection method can be used and in this case, the G equals to three times the value of shunt resistance(s).
D. `1/3` deflection method can be used and in this case the G value equals to the shunt resistance(s).

Explanation

To determine the resistance \( G \) of a galvanometer using the 1/3 deflection method, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
The galvanometer has a resistance \( G \) and is connected in a circuit with a known resistance \( S \). The current flowing through the circuit causes a deflection in the galvanometer.

2. **Deflection Condition**:
For a galvanometer, the deflection \( \theta \) is proportional to the current \( I_g \) flowing through it. The relationship can be expressed as:
\[ \frac{I_g}{I} = \frac{S}{S + G} \]
where \( I \) is the total current in the circuit.

3. **Using the 1/3 Deflection**:
Given that the deflection is \( \frac{1}{3} \), we can set up the equation:
\[ \frac{I_g}{I} = \frac{1}{3} \]
This implies:
\[ \frac{S}{S + G} = \frac{1}{3} \]

4. **Cross-Multiplying**:
Cross-multiplying gives:
\[ 3S = S + G \]

5. **Rearranging the Equation**:
Rearranging the equation results in:
\[ G = 3S - S = 2S \]

6. **Conclusion**:
Thus, the resistance \( G \) of the galvanometer is twice the resistance \( S \) of the standard resistor used in the circuit.

### Final Result:
The correct statement regarding the measurement of \( G \) using the 1/3 deflection method is:
\[ G = 2S \]