A galvaometer of coil resistance `100Omega` is connected to a shunt of resistance `10Omega`. The current throught the galvanometer is `i_(10` , the current through the shunt is `i_(2)` and the total current into the combination is `i_(3)`, then the ratio `i_(1):i_(2):i_(3)` is

Options

A. `1:10:11`
B. `10:1:11`
C. `11:10:1`
D. `10:11:1`

Explanation

To solve the problem, we need to find the ratio of the currents through the galvanometer (I1), the shunt (I2), and the total current (I3).

### Step-by-Step Solution:

1. **Identify the Resistances**:
- Resistance of the galvanometer (Rg) = 100 Ω
- Resistance of the shunt (Rs) = 10 Ω

2. **Understanding the Current Relationships**:
- The current through the galvanometer is denoted as I1.
- The current through the shunt is denoted as I2.
- The total current entering the combination is denoted as I3.

3. **Using the Current Division Rule**:
- The current through the galvanometer (I1) can be expressed in terms of the total current (I3) using the formula:
\[ I1 = \frac{Rs}{Rs + Rg} \cdot I3 \]
- Substituting the values:
\[ I1 = \frac{10}{10 + 100} \cdot I3 = \frac{10}{110} \cdot I3 = \frac{1}{11} \cdot I3 \]

4. **Finding the Current through the Shunt (I2)**:
- The current through the shunt (I2) can be calculated using:
\[ I2 = I3 - I1 \]
- Substituting I1 from the previous step:
\[ I2 = I3 - \frac{1}{11} I3 = \frac{11}{11} I3 - \frac{1}{11} I3 = \frac{10}{11} I3 \]

5. **Expressing the Ratios**:
- Now we have:
\[ I1 = \frac{1}{11} I3 \]
\[ I2 = \frac{10}{11} I3 \]
- To find the ratio \( I1 : I2 : I3 \), we can express everything in terms of I3:
\[ I1 : I2 : I3 = \frac{1}{11} I3 : \frac{10}{11} I3 : I3 \]
- Dividing each term by I3 gives:
\[ I1 : I2 : I3 = \frac{1}{11} : \frac{10}{11} : 1 \]
- To eliminate the fractions, we multiply through by 11:
\[ I1 : I2 : I3 = 1 : 10 : 11 \]

### Final Answer:
The ratio \( I1 : I2 : I3 \) is \( 1 : 10 : 11 \).