The resistance of a moving coil galvanometer is `20Omega`. It requires 0.01 A current for full - scale deflection. The value of resistance to convert it into a voltmeter of the range 20 V will be

Options

A. `198Omega`
B. `1980Omega`
C. `20Omega`
D. `0Omega`

Answer

To solve the problem of converting a moving coil galvanometer into a voltmeter, we need to determine the additional resistance required in series with the galvanometer. Here’s a step-by-step solution:

### Step 1: Understand the Given Data
- The resistance of the galvanometer (G) = 20 Ω
- The current required for full-scale deflection (I_G) = 0.01 A
- The desired voltage range for the voltmeter (V) = 20 V

### Step 2: Use Ohm's Law
To convert the galvanometer into a voltmeter, we need to find the total resistance (R_total) required for the voltmeter to measure up to 20 V with the specified current.

Using Ohm's Law:
\[ V = I \cdot R_{total} \]

Where:
- \( V \) is the voltage across the voltmeter.
- \( I \) is the current through the circuit (which is the same as I_G for full-scale deflection).
- \( R_{total} \) is the total resistance of the circuit (which is the sum of the galvanometer resistance and the additional resistance).

### Step 3: Calculate Total Resistance
From the equation, we can express \( R_{total} \) as:
\[ R_{total} = \frac{V}{I_G} \]

Substituting the known values:
\[ R_{total} = \frac{20 \, \text{V}}{0.01 \, \text{A}} = 2000 \, \Omega \]

### Step 4: Calculate the Additional Resistance
The total resistance required for the voltmeter is the sum of the galvanometer resistance and the additional resistance (R):
\[ R_{total} = R + G \]

Rearranging gives us:
\[ R = R_{total} - G \]

Substituting the values we have:
\[ R = 2000 \, \Omega - 20 \, \Omega = 1980 \, \Omega \]

### Step 5: Conclusion
The value of the resistance required to convert the galvanometer into a voltmeter of range 20 V is:
\[ R = 1980 \, \Omega \]

### Final Answer
The required resistance is **1980 Ω**.

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