A galvanometer having a coil resistance of `100 omega` gives a full scale deflection , when a current of `1 mA` is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of `10A` , is :

Options

A. `0.1 omega`
B. ` 3 omega`
C. ` 0.01 omega`
D. ` 2 omega`

Explanation

To solve the problem of converting a galvanometer into an ammeter, we need to find the resistance (S) that should be connected in parallel with the galvanometer. Here’s a step-by-step solution:

### Step 1: Understand the given data
- The galvanometer has a coil resistance (G) = 100 ohms.
- The galvanometer gives full-scale deflection at a current (Ig) = 1 mA = 0.001 A.
- We want to convert it to an ammeter that gives full-scale deflection at a current (I) = 10 A.

### Step 2: Use the formula for voltage across the galvanometer and shunt
When a current I flows through the circuit, part of it (Ig) flows through the galvanometer and the rest (I - Ig) flows through the shunt resistance (S). The voltage drop across both the galvanometer and the shunt must be equal. Thus, we can write:

\[ Ig \cdot G = (I - Ig) \cdot S \]

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:

\[ 0.001 \cdot 100 = (10 - 0.001) \cdot S \]

This simplifies to:

\[ 0.1 = 9.999 \cdot S \]

### Step 4: Solve for S
Now, we can solve for S:

\[ S = \frac{0.1}{9.999} \]

Calculating this gives:

\[ S \approx 0.01 \, \text{ohms} \]

### Step 5: Conclusion
The resistance that should be connected in parallel with the galvanometer to convert it into an ammeter that gives full-scale deflection at 10 A is approximately **0.01 ohms**.

### Final Answer
The required resistance (S) is **0.01 ohms**.

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