A moving coil galvnometer is converted into an ammeter reading up to `0.03 A` by connecting a shunt of resistance `r/4`. What is the maximum current which can be sent through this galvanometer if no shunt is used (here r=resistance of galvanometer)

Options

A. `0.004A`
B. `0.005A`
C. `0.006A`
D. `0.008A`

Explanation

To solve the problem, we need to determine the maximum current that can pass through the galvanometer without the shunt resistance. We will use the information provided about the shunt resistance and the current readings.

### Step-by-step Solution:

1. **Understanding the Setup**:
- Let the resistance of the galvanometer be \( R \).
- The shunt resistance connected is \( \frac{R}{4} \).
- The maximum current that can be measured by the ammeter (which includes the galvanometer and the shunt) is \( 0.03 \, A \).

2. **Current Division**:
- When the total current \( I \) (which is \( 0.03 \, A \)) flows through the circuit, part of it \( I_G \) flows through the galvanometer and the remaining \( 0.03 - I_G \) flows through the shunt.

3. **Applying Kirchhoff's Law**:
- The potential drop across the galvanometer and the shunt must be equal since they are in parallel.
- The potential drop across the galvanometer is given by:
\[ V = I_G \cdot R \]
- The potential drop across the shunt is given by:
\[ V = (0.03 - I_G) \cdot \frac{R}{4} \]

4. **Setting the Equations Equal**:
- Setting the two expressions for potential drop equal gives:
\[ I_G \cdot R = (0.03 - I_G) \cdot \frac{R}{4} \]

5. **Simplifying the Equation**:
- We can cancel \( R \) from both sides (assuming \( R \neq 0 \)):
\[ I_G = (0.03 - I_G) \cdot \frac{1}{4} \]
- Multiplying through by 4:
\[ 4 I_G = 0.03 - I_G \]
- Rearranging gives:
\[ 5 I_G = 0.03 \]

6. **Solving for \( I_G \)**:
- Dividing both sides by 5:
\[ I_G = \frac{0.03}{5} = 0.006 \, A \]

7. **Conclusion**:
- The maximum current that can be sent through the galvanometer without the shunt is \( 0.006 \, A \).

### Final Answer:
The maximum current that can be sent through the galvanometer without the shunt is **0.006 A**.