The fraction of the total current passing through the galvanometer is ……………

Options

A. ` ( S ) /( S + G) `
B. ` ( G) /( S + G ) `
C. ` ( S + G ) /( G) `
D. ` ( S + G) / ( S ) `

Answer

To find the fraction of the total current passing through the galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- A galvanometer is connected in parallel with a shunt resistor. Let the total current supplied be \( I_0 \).

2. **Current Distribution**:
- The total current \( I_0 \) splits into two parts:
- \( I \): the current passing through the galvanometer
- \( I_0 - I \): the current passing through the shunt resistor

3. **Voltage Drop Across Components**:
- Since the galvanometer and the shunt are in parallel, the voltage drop across both must be equal.
- Let \( S \) be the shunt resistance and \( G \) be the galvanometer resistance.
- The voltage drop across the shunt can be expressed as:
\[ V = (I_0 - I) \cdot S \]
- The voltage drop across the galvanometer can be expressed as:
\[ V = I \cdot G \]

4. **Setting the Voltage Drops Equal**:
- Since the voltage drops are equal, we can set the equations equal to each other:
\[ (I_0 - I) \cdot S = I \cdot G \]

5. **Rearranging the Equation**:
- Expanding and rearranging gives:
\[ I_0 S - I S = I G \]
- Rearranging further, we have:
\[ I_0 S = I (G + S) \]

6. **Solving for Current through the Galvanometer**:
- We can isolate \( I \):
\[ I = \frac{I_0 S}{G + S} \]

7. **Finding the Fraction of Total Current**:
- The fraction of the total current passing through the galvanometer is given by:
\[ \frac{I}{I_0} = \frac{\frac{I_0 S}{G + S}}{I_0} = \frac{S}{G + S} \]

### Final Answer:
The fraction of the total current passing through the galvanometer is:
\[ \frac{S}{G + S} \]