A galvanometer having a resistance of `50Omega` , gives a full scale deflection for a current if `0.05` A. The length in metre if a resistance wire of area of cross- section `2.97 xx10^-2cm^2` that can be used to convert the gaivanometer into an ammeter which can read a maximum of 5 A current is (specific resistance of the wire =`5xx10^-7Omega-m`)

Options

A. 9
B. 6
C. 3
D. 1.5

Answer

To solve the problem step-by-step, we need to determine the length of the resistance wire required to convert the galvanometer into an ammeter that can read a maximum current of 5 A.

### Step 1: Calculate the Shunt Resistance (S)
The formula for the shunt resistance \( S \) needed to convert a galvanometer into an ammeter is given by:

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

Where:
- \( I_g = 0.05 \, A \) (full-scale deflection current of the galvanometer)
- \( G = 50 \, \Omega \) (resistance of the galvanometer)
- \( I = 5 \, A \) (maximum current to be measured)

Substituting the values:

\[ S = \frac{0.05 \cdot 50}{5 - 0.05} \]

Calculating the denominator:

\[ 5 - 0.05 = 4.95 \]

Now substituting back:

\[ S = \frac{2.5}{4.95} \approx 0.505 \, \Omega \]

### Step 2: Use the Shunt Resistance to Find the Length of the Wire
The resistance \( R \) of the wire can be calculated using the formula:

\[ R = \frac{\rho \cdot l}{A} \]

Where:
- \( \rho = 5 \times 10^{-7} \, \Omega \cdot m \) (specific resistance of the wire)
- \( A = 2.97 \times 10^{-2} \, cm^2 = 2.97 \times 10^{-6} \, m^2 \) (cross-sectional area converted to m²)
- \( l \) is the length of the wire we need to find.

Rearranging the formula to solve for \( l \):

\[ l = \frac{R \cdot A}{\rho} \]

Substituting the values:

\[ l = \frac{0.505 \cdot 2.97 \times 10^{-6}}{5 \times 10^{-7}} \]

Calculating the numerator:

\[ 0.505 \cdot 2.97 \times 10^{-6} \approx 1.5 \times 10^{-6} \]

Now substituting back into the equation:

\[ l = \frac{1.5 \times 10^{-6}}{5 \times 10^{-7}} = 3 \, m \]

### Final Answer
The length of the resistance wire required is approximately **3 meters**.

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