Question

A voltmeter of resistance \(400 \, \Omega\) is used to measure the emf of a cell with an internal resistance of \(4 \, \Omega\). The error in the measurement of emf of the cell is:

• A. 1.01%
• B. 2.01%
• C. 1.99%
• D. 0.99%

Hint:

Using a voltmeter with a much higher resistance than the internal resistance of the cell minimizes measurement errors.

Answer 1

The Correct Option is D

The total resistance \( R_t \), when the voltmeter is connected in parallel with the cell's internal resistance, is given by the parallel resistance formula: \[ R_t = \frac{R_{\text{internal}} \cdot R_{\text{voltmeter}}}{R_{\text{internal}} + R_{\text{voltmeter}}} = \frac{4 \cdot 400}{4 + 400} \approx 3.922 \, \Omega \] The error percentage is then calculated as: \[ \text{Error} = \left(1 - \frac{R_{\text{internal}}}{R_t}\right) \times 100 \approx 0.99\% \]