The full scale deflection current of a galvanometer of resistance `1Omega` is `5 mA`. How will you convert it into a voltmeter of range of ` 5V`?

Explanation

To convert a galvanometer into a voltmeter, we need to determine the shunt resistance that must be added in series with the galvanometer. Here’s a step-by-step solution:

### Step 1: Identify Given Values
- Full-scale deflection current of the galvanometer (Ig) = 5 mA = \(5 \times 10^{-3}\) A
- Resistance of the galvanometer (Rg) = 1 Ω
- Desired voltage range of the voltmeter (V) = 5 V

### Step 2: Use Ohm's Law
The voltage across the galvanometer when it shows full-scale deflection can be calculated using Ohm's Law:
\[ V = I_g \times R_g \]
Substituting the values:
\[ V = (5 \times 10^{-3} \, \text{A}) \times (1 \, \Omega) = 5 \times 10^{-3} \, \text{V} = 0.005 \, \text{V} \]

### Step 3: Calculate Total Resistance for the Desired Voltage
To convert the galvanometer into a voltmeter that can measure up to 5 V, we need to find the total resistance (R_total) that will allow the full-scale deflection current to flow at this voltage:
\[ R_{\text{total}} = \frac{V}{I_g} = \frac{5 \, \text{V}}{5 \times 10^{-3} \, \text{A}} = 1000 \, \Omega \]

### Step 4: Calculate the Shunt Resistance
The total resistance in the circuit when the shunt resistance (S) is added in series with the galvanometer is:
\[ R_{\text{total}} = R_g + S \]
Rearranging gives:
\[ S = R_{\text{total}} - R_g = 1000 \, \Omega - 1 \, \Omega = 999 \, \Omega \]

### Conclusion
The shunt resistance required to convert the galvanometer into a voltmeter with a range of 5 V is:
\[ S = 999 \, \Omega \]