In `Q.36`, the combined resistance of the shunt and the galvanometer is

Options

A. `3665 Omega`
B. `111 Omega`
C. `107.7 Omega`
D. `3555.3 Omega`

Explanation

To solve the question regarding the combined resistance of the shunt and the galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Resistance of the galvanometer (G) = 3663 ohms
- Current through the galvanometer (Ig) = 1/34 of total current (I)
- Shunt resistance (S) = 111 ohms (as calculated in the previous question)

2. **Understanding the Circuit Configuration:**
- The shunt (S) and galvanometer (G) are connected in parallel.

3. **Formula for Equivalent Resistance in Parallel:**
- The formula for the equivalent resistance (R_eq) of two resistances in parallel is given by:
\[ \frac{1}{R_{eq}} = \frac{1}{S} + \frac{1}{G} \]
- This can be rearranged to:
\[ R_{eq} = \frac{S \cdot G}{S + G} \]

4. **Substituting the Values:**
- Substitute S = 111 ohms and G = 3663 ohms into the formula:
\[ R_{eq} = \frac{111 \cdot 3663}{111 + 3663} \]

5. **Calculating the Denominator:**
- Calculate \( S + G \):
\[ 111 + 3663 = 3774 \]

6. **Calculating the Numerator:**
- Calculate \( S \cdot G \):
\[ 111 \cdot 3663 = 406653 \]

7. **Final Calculation of Equivalent Resistance:**
- Now, substitute the values back into the equation:
\[ R_{eq} = \frac{406653}{3774} \approx 107.7 \text{ ohms} \]

8. **Conclusion:**
- The combined resistance of the shunt and the galvanometer is approximately 107.7 ohms.

### Final Answer:
The combined resistance of the shunt and the galvanometer is **107.7 ohms**.