Question

A voltmeter of resistance 1000 \( \Omega \) can measure up to 25 V. How will you convert it so that it can read up to 250 V?

Hint:

To extend the voltage range of a voltmeter, a series resistor is used. The value of the series resistor is calculated by the voltage division rule. Make sure to use a resistor with appropriate power rating to avoid overheating.

Answer 1

To convert the voltmeter so that it can measure up to 250 V, we use a series resistor. Let the series resistance be \( R_s \), and the total resistance should be such that the voltmeter can measure 250 V when the original meter reads 25 V. Using the formula for voltage division: \[ V_{\text{new}} = V_{\text{max}} \times \frac{R_{\text{meter}}}{R_{\text{meter}} + R_s} \] Where:
- \( V_{\text{new}} \) is the new voltage range (250 V),
- \( V_{\text{max}} \) is the original maximum voltage (25 V),
- \( R_{\text{meter}} \) is the resistance of the voltmeter (1000 \( \Omega \)). We can rearrange the formula to solve for \( R_s \): \[ \frac{250}{25} = \frac{1000}{1000 + R_s} \] Simplifying: \[ 10 = \frac{1000}{1000 + R_s} \] Now, solve for \( R_s \): \[ 10 (1000 + R_s) = 1000 \] \[ 10000 + 10 R_s = 1000 \] \[ 10 R_s = 1000
- 10000 = 9000 \] \[ R_s = 9000 \, \Omega \] Thus, the required series resistance is \( 9000 \, \Omega \).