A galvanometer has a a coil resistance 100 ohm and gives a full scale deflection for 30 mA current. If it is to work as a voltmeter of 30 volt rang, the resistance required to be added will be

Options

A. `900 Omega `
B. `1800 Omega `
C. `500 Omega `
D. `1000 Omega `

Explanation

To solve the problem step by step, we need to determine the resistance required to be added to the galvanometer in order to use it as a voltmeter with a range of 30 volts.

### Step 1: Understand the given values
- **Coil resistance of galvanometer (R_g)** = 100 ohms
- **Full scale deflection current (I_g)** = 30 mA = 30 × 10^(-3) A
- **Desired voltage range (V)** = 30 V

### Step 2: Calculate the voltage across the galvanometer at full scale deflection
Using Ohm's law, the voltage across the galvanometer (V_g) when the full scale deflection current flows through it can be calculated as:
\[ V_g = I_g \times R_g \]
Substituting the values:
\[ V_g = 30 \times 10^{-3} \, \text{A} \times 100 \, \text{ohms} = 3 \, \text{V} \]

### Step 3: Determine the total voltage required
Since we want to use the galvanometer as a voltmeter for a range of 30 V, we need to find the additional voltage that must be dropped across the added resistance (R).

### Step 4: Calculate the additional voltage needed
The additional voltage (V_R) that needs to be dropped across the added resistance is:
\[ V_R = V - V_g = 30 \, \text{V} - 3 \, \text{V} = 27 \, \text{V} \]

### Step 5: Use Ohm's law to find the required resistance
The total current flowing through the circuit remains the same (I_g = 30 mA). We can use Ohm's law to find the resistance (R) that needs to be added in series:
\[ V_R = I_g \times R \]
Rearranging the equation gives:
\[ R = \frac{V_R}{I_g} \]
Substituting the values:
\[ R = \frac{27 \, \text{V}}{30 \times 10^{-3} \, \text{A}} = \frac{27}{0.03} = 900 \, \text{ohms} \]

### Step 6: Conclusion
The resistance required to be added in series with the galvanometer to convert it into a voltmeter with a range of 30 V is **900 ohms**.

### Final Answer
**900 ohms**

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