A galvanometer coil has a resistance of 10A and the meter shows full scale deflection for a current of 1mA. The shunt resistance required to convert the galvanometer into an ammeter of range 0-100mA is about

Options

A. `10 Omega `
B. `1 Omega `
C. `0.1 Omega `
D. `0.01 Omega `

Explanation

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

### Step 1: Understand the Given Information
- The resistance of the galvanometer coil (Rg) = 10 Ω
- The full-scale deflection current (Ig) = 1 mA = 0.001 A
- The desired maximum current for the ammeter (I) = 100 mA = 0.1 A

### Step 2: Determine the Current through the Shunt Resistor
The current through the shunt resistor (Is) can be calculated using the formula:
\[ I = I_g + I_s \]
Where:
- \( I \) is the total current (0.1 A)
- \( I_g \) is the galvanometer current (0.001 A)
- \( I_s \) is the current through the shunt resistor

Rearranging gives:
\[ I_s = I - I_g = 0.1 A - 0.001 A = 0.099 A \]

### Step 3: Apply the Formula for Shunt Resistance
The shunt resistance (Rs) can be calculated using the formula:
\[ R_s = \frac{R_g \cdot I_g}{I_s} \]
Where:
- \( R_g \) is the resistance of the galvanometer (10 Ω)
- \( I_g \) is the galvanometer current (0.001 A)
- \( I_s \) is the current through the shunt (0.099 A)

### Step 4: Substitute the Values into the Formula
Substituting the known values into the formula:
\[ R_s = \frac{10 \cdot 0.001}{0.099} \]

### Step 5: Calculate the Shunt Resistance
Calculating the above expression:
\[ R_s = \frac{0.01}{0.099} \approx 0.10101 \, \Omega \]

### Step 6: Round the Result
Rounding this value gives:
\[ R_s \approx 0.1 \, \Omega \]

### Final Answer
The required shunt resistance to convert the galvanometer into an ammeter of range 0-100 mA is approximately **0.1 Ω**.

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