A voltmeter has resistance `2000 Omega` and range 5 V. For increasing its range upto 20V, a resistance of

Options

A. `8000 Omega ` should be connected in series.
B. `6000 Omega ` should be connected in series.
C. `8000 Omega ` should be connected in parallel
D. `6000 Omega ` should be connected in parallel.

Answer

To solve the problem of increasing the range of a voltmeter from 5V to 20V by adding a resistance, we can follow these steps:

### Step 1: Understand the given values
- The resistance of the voltmeter (R) is given as \(2000 \, \Omega\).
- The initial range of the voltmeter is \(5 \, V\).
- We want to increase the range to \(20 \, V\).

### Step 2: Determine the current through the voltmeter
The current through the voltmeter when it reads \(5V\) can be calculated using Ohm's law:
\[ I_G = \frac{V}{R} = \frac{5 \, V}{2000 \, \Omega} = \frac{5}{2000} = 0.0025 \, A \]

### Step 3: Set up the equation for the new range
To find the new resistance \(R_s\) needed to achieve a range of \(20V\), we use the formula:
\[ V = I_G \times R_s \]
Where \(V\) is the new voltage range (20V) and \(I_G\) is the current through the voltmeter.

### Step 4: Substitute the known values into the equation
We already calculated \(I_G\) as \(0.0025 \, A\). Now we can substitute \(V = 20V\) into the equation:
\[ 20 = 0.0025 \times R_s \]

### Step 5: Solve for \(R_s\)
Rearranging the equation gives:
\[ R_s = \frac{20}{0.0025} = 8000 \, \Omega \]

### Step 6: Conclusion
The resistance that needs to be added in series to increase the range of the voltmeter to \(20V\) is \(8000 \, \Omega\).

### Final Answer:
The resistance required to increase the range of the voltmeter to \(20V\) is \(8000 \, \Omega\).

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