A galvanometer of resistance `100Omega` gives full deffection for a current `10^(-5)` the value of shunt required to convert it into ammeter of range 1 ampere is:-

Options

A. The centre of mass of plank-man system remains stationary
B. The plank will slide to the north by a dsitance `4m`
C. The plank will slide to the south by a distance `4 m`
D. The plank will slide to the south by a distance `12 m`

Explanation

To solve the problem, we need to find the value of the shunt resistance required to convert a galvanometer into an ammeter with a specified range. Here are the steps to arrive at the solution:

### Step 1: Understand the given values
- Resistance of the galvanometer (Rg) = 100 Ω
- Full-scale deflection current of the galvanometer (Ig) = \(10^{-5}\) A
- Desired range of the ammeter (I) = 1 A

### Step 2: Use the formula for shunt resistance
The formula to calculate the shunt resistance (S) required to convert a galvanometer into an ammeter is given by:

\[ S = \frac{I_g \cdot R_g}{I - I_g} \]

Where:
- \(I_g\) is the full-scale deflection current of the galvanometer,
- \(R_g\) is the resistance of the galvanometer,
- \(I\) is the total current through the ammeter.

### Step 3: Substitute the known values into the formula
Substituting the values we have:

\[ S = \frac{(10^{-5} \, \text{A}) \cdot (100 \, \Omega)}{1 \, \text{A} - 10^{-5} \, \text{A}} \]

### Step 4: Simplify the equation
Calculating the numerator:

\[ (10^{-5} \, \text{A}) \cdot (100 \, \Omega) = 10^{-3} \, \text{V} \]

Now, calculating the denominator:

\[ 1 \, \text{A} - 10^{-5} \, \text{A} \approx 1 \, \text{A} \quad (\text{since } 10^{-5} \text{ is very small compared to } 1) \]

### Step 5: Calculate the shunt resistance
Now, substituting back into the formula:

\[ S = \frac{10^{-3} \, \text{V}}{1 \, \text{A}} = 10^{-3} \, \Omega \]

### Final Answer
Thus, the value of the shunt required is:

\[ S = 10^{-3} \, \Omega \]