The resistance of a galvanometer coil is R. What is the shunt resistance required to convert it into an ammeter of range 4 times

Options

A. R/5
B. R/4
C. R/3
D. 4R

Explanation

To solve the problem of finding the shunt resistance required to convert a galvanometer into an ammeter with a range 4 times that of the galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**:
- We have a galvanometer with a resistance \( R \).
- We need to find the shunt resistance \( R' \) required to convert it into an ammeter with a range that is 4 times the original current range of the galvanometer.

2. **Define Initial Conditions**:
- Let the initial current through the galvanometer be \( I_0 \).
- The voltage across the galvanometer when it carries current \( I_0 \) is given by Ohm's law:
\[ V = I_0 R \]

3. **New Conditions with Shunt Resistance**:
- When we connect a shunt resistance \( R' \) in parallel with the galvanometer, the total current \( I \) flowing through the circuit will be \( 4 I_0 \) (as the range is 4 times).
- The current through the galvanometer will still be \( I_0 \), and the current through the shunt resistance will be \( I' = I - I_0 = 4 I_0 - I_0 = 3 I_0 \).

4. **Voltage Across the Shunt and Galvanometer**:
- Since the galvanometer and the shunt are in parallel, the voltage across both is the same:
\[ V = I_0 R = I' R' = 3 I_0 R' \]

5. **Set Up the Equation**:
- From the above, we can equate the two expressions for voltage:
\[ I_0 R = 3 I_0 R' \]
- Dividing both sides by \( I_0 \) (assuming \( I_0 \neq 0 \)):
\[ R = 3 R' \]

6. **Solve for Shunt Resistance**:
- Rearranging the equation gives:
\[ R' = \frac{R}{3} \]

### Final Answer:
The shunt resistance required to convert the galvanometer into an ammeter with a range 4 times that of the galvanometer is:
\[ R' = \frac{R}{3} \]