Calculate the value of the shunt resistance when connected across a galvanometer of resistance `18Omega` will allow 1/10 th of the current to pass through the galvanometer.

Answer

To solve the problem of calculating the value of the shunt resistance (S) connected across a galvanometer with a resistance (G) of 18 ohms, which allows 1/10th of the current to pass through the galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- The galvanometer (G) has a resistance of 18 ohms.
- We want 1/10th of the total current (I) to pass through the galvanometer. Therefore, the current through the galvanometer (Ig) is given by:
\[ I_g = \frac{I}{10} \]

2. **Apply the Formula for Current Division**:
- The relationship between the total current (I), the current through the galvanometer (Ig), and the shunt resistance (S) can be expressed using the formula:
\[ I_g = \frac{I \cdot S}{S + G} \]
- Here, G is the resistance of the galvanometer (18 ohms).

3. **Substitute Known Values**:
- Substitute \( I_g = \frac{I}{10} \) and \( G = 18 \) into the formula:
\[ \frac{I}{10} = \frac{I \cdot S}{S + 18} \]

4. **Eliminate I from the Equation**:
- Since I appears on both sides, we can cancel it out (assuming \( I \neq 0 \)):
\[ \frac{1}{10} = \frac{S}{S + 18} \]

5. **Cross-Multiply to Solve for S**:
- Cross-multiplying gives:
\[ 1 \cdot (S + 18) = 10S \]
- This simplifies to:
\[ S + 18 = 10S \]

6. **Rearrange the Equation**:
- Rearranging the equation gives:
\[ 18 = 10S - S \]
\[ 18 = 9S \]

7. **Solve for S**:
- Dividing both sides by 9 gives:
\[ S = \frac{18}{9} = 2 \, \text{ohms} \]

### Final Answer:
The value of the shunt resistance \( S \) is **2 ohms**.

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