A galvanometer with a coil of resistance `50 Omega` shows full-scale deflection when 10 mA current passes through it.

Options

A. The galvanometer can measure a maximum voltage of 0.5 V.
B. 5 A current can be measured if a shunt of `0.1 Omega` is connected in parallel to it.
C. It can be used as voltmeter to measure a voltage of 5 V if `450 Omega` resistance is connected in series with the coil of the galvanometer.
D. It can be used as a voltmeter to measure a voltage of 50 V if `4,950 Omega` resistance is connected in series with the coil of the galvanometer.

Explanation

To solve the problem step by step, we will analyze the given information about the galvanometer and determine the maximum voltage it can measure, as well as the shunt resistance required for measuring higher currents.

### Step 1: Calculate the maximum voltage that the galvanometer can measure.

The formula for the voltage across the galvanometer is given by:
\[ V_g = I_g \times R_g \]
Where:
- \( V_g \) = voltage across the galvanometer
- \( I_g \) = current for full-scale deflection (10 mA = \( 10 \times 10^{-3} \) A)
- \( R_g \) = resistance of the galvanometer (50 Ω)

Substituting the values:
\[ V_g = (10 \times 10^{-3}) \times 50 \]
\[ V_g = 0.5 \, \text{V} \]

### Step 2: Determine if a shunt of 0.1 Ω can allow the galvanometer to measure 5 A.

To convert the galvanometer into an ammeter that can measure 5 A, we need to find the required shunt resistance \( R_s \).

Using the formula:
\[ I = I_g + I_s \]
Where:
- \( I \) = total current (5 A)
- \( I_g \) = current through the galvanometer (10 mA = \( 10 \times 10^{-3} \) A)
- \( I_s \) = current through the shunt

Thus,
\[ I_s = I - I_g = 5 - 0.01 = 4.99 \, \text{A} \]

The voltage across the galvanometer and the shunt must be the same:
\[ I_g \times R_g = I_s \times R_s \]

Substituting the known values:
\[ (10 \times 10^{-3}) \times 50 = 4.99 \times R_s \]
\[ 0.5 = 4.99 \times R_s \]

Now, solving for \( R_s \):
\[ R_s = \frac{0.5}{4.99} \approx 0.1002 \, \Omega \]

This is approximately equal to 0.1 Ω, confirming that the second option is correct.

### Step 3: Determine if the galvanometer can be used as a voltmeter for 5 V and 15 V.

To use the galvanometer as a voltmeter, we can connect a suitable shunt resistance in series. The voltage that can be measured depends on the total resistance in the circuit.

For a voltmeter, the maximum voltage \( V \) that can be measured is given by:
\[ V = I_g \times (R_g + R_s) \]

For both 5 V and 15 V, we can choose appropriate values for \( R_s \) such that:
- If we want to measure 5 V, we can find a suitable \( R_s \).
- If we want to measure 15 V, we can also find a suitable \( R_s \).

Since theoretically, we can adjust \( R_s \) to achieve any desired voltage, both options C and D are also correct.

### Final Conclusion:
All four options (A, B, C, and D) are correct.

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