A galvanometer of resistance 15 `ohm` gives full scale deflection for a current of 2 mA. Calculate the shunt resistance needed to convert it into an ammeter of range 0 to 5 A

Options

A. `0.712ohm`
B. `1.203ohm`
C. `0.006ohm`
D. `0.015 ohm`

Answer

To solve the problem of finding the shunt resistance needed to convert a galvanometer into an ammeter, we can follow these steps:

### Step 1: Identify the given values
- Resistance of the galvanometer, \( R_G = 15 \, \Omega \)
- Full-scale deflection current of the galvanometer, \( I_G = 2 \, \text{mA} = 0.002 \, \text{A} \)
- Desired range of the ammeter, \( I = 5 \, \text{A} \)

### Step 2: Calculate the current through the shunt
The current that will pass through the shunt resistor \( R_S \) can be calculated using the formula:
\[ I_S = I - I_G \]
Where:
- \( I_S \) is the current through the shunt resistor.

Substituting the values:
\[ I_S = 5 \, \text{A} - 0.002 \, \text{A} = 4.998 \, \text{A} \]

### Step 3: Use the formula for shunt resistance
The shunt resistance \( R_S \) can be calculated using the formula:
\[ R_S = \frac{R_G \cdot I_G}{I_S} \]
Substituting the values:
\[ R_S = \frac{15 \, \Omega \cdot 0.002 \, \text{A}}{4.998 \, \text{A}} \]

### Step 4: Calculate \( R_S \)
Now, we perform the calculations:
\[ R_S = \frac{0.03 \, \Omega \cdot \text{A}}{4.998 \, \text{A}} \approx 0.006002 \, \Omega \]

### Step 5: Final answer
Thus, the shunt resistance needed to convert the galvanometer into an ammeter of range 0 to 5 A is approximately:
\[ R_S \approx 0.006 \, \Omega \]