Question

A voltmeter of resistance $1000 \, \Omega $ and $0.5 \, \text{V/div} $ is to be converted into a voltmeter to make it read $1 \, \text{V/div} $. The value of high resistance to be connected in series with it is

• A. 6000 \( \Omega \)
• B. 5000 \( \Omega \)
• C. 4000 \( \Omega \)
• D. 1000 \( \Omega \)

Hint:

When converting a voltmeter for different sensitivities, adjust the total resistance by calculating the required series resistance based on the ratio of the original and desired sensitivity.

Answer 1

The Correct Option is D

To adjust the voltmeter so that it reads \(1 \, \text{V/div}\), we need to increase its sensitivity. Since the initial setting is \(0.5 \, \text{V/div}\), the series resistance must double the voltage per division. The formula for the total resistance is: \[ R_{\text{total}} = R_{\text{original}} + R_{\text{series}} \] For the voltage to read \(1 \, \text{V/div}\), the total resistance must be doubled. Since the original resistance is \(1000 \, \Omega\), the new resistance needed is \(2000 \, \Omega\).
Thus, the value of the series resistance required is: \[ R_{\text{series}} = 2000 \, \Omega - 1000 \, \Omega = 1000 \, \Omega \] Therefore, the value of the high resistance to be connected in series is \(1000 \, \Omega\).