The range of voltmeter is 10 V and its internal resistance is `50 Omega`. To convert it to voltmeter of range 15 V, how much resistance is to be added ?

Options

A. Add `25 Omega` resistor in parallel
B. Add `25 Omega` resistor in series
C. Add `125 Omega` resistor in parallel
D. Add `125 Omega` resistor in series

Answer

To convert a voltmeter with a range of 10 V and an internal resistance of 50 Ω into a voltmeter with a range of 15 V, we need to follow these steps:

### Step 1: Understand the basic principle of a voltmeter
A voltmeter is essentially a galvanometer with a resistance connected in series. The total resistance of the voltmeter determines the voltage range it can measure.

### Step 2: Calculate the current through the galvanometer
The current (I) through the galvanometer when measuring 10 V can be calculated using Ohm's law:
\[ I = \frac{V}{R} = \frac{10 \, \text{V}}{50 \, \Omega} = 0.2 \, \text{A} \]

### Step 3: Set up the equation for the new range
When we want to convert the voltmeter to a range of 15 V, we assume the current through the galvanometer remains the same (0.2 A). We can set up the equation:
\[ I = \frac{V_{new}}{R_{new}} \]
Substituting the values:
\[ 0.2 = \frac{15}{R_{new}} \]

### Step 4: Solve for the new resistance
Rearranging the equation to find \( R_{new} \):
\[ R_{new} = \frac{15}{0.2} = 75 \, \Omega \]

### Step 5: Determine the additional resistance needed
The original internal resistance of the voltmeter is 50 Ω. To find the additional resistance (R_add) needed to achieve the new total resistance:
\[ R_{add} = R_{new} - R_{original} = 75 \, \Omega - 50 \, \Omega = 25 \, \Omega \]

### Conclusion
To convert the voltmeter from a range of 10 V to 15 V, we need to add a resistance of 25 Ω in series.

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