Question

A voltmeter with internal resistance of \(x\) Ω can be used to measure upto 20 V. In order to increase its measuring range to 30 V, the required modification is to ________.

• A. connect resistor of \(\frac{x}{2}\) Ω, in series with voltmeter.
• B. connect resistor of \(\frac{x}{2}\) Ω, in parallel to voltmeter.
• C. connect a resistor of \(x\) Ω in series with voltmeter.
• D. connect resistor of \(2x\) Ω in parallel to voltmeter.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
To increase the range of a voltmeter, a high resistance (multiplier) must be connected in series. This ensures that for a higher total voltage, the current through the voltmeter remains within its original safe operating limit ($I_g$).

Step 2: Key Formula or Approach:
1. Full-scale current $I_g = \frac{V_{old}}{G} = \frac{20}{x}$. 2. New range $V_{new} = I_g(G + R_{series})$.

Step 3: Detailed Explanation:
1. We want to measure $V' = 30$ V using the same $I_g$. 2. $30 = \frac{20}{x} (x + R)$ 3. Divide by 10: $3 = \frac{2}{x}(x + R)$ 4. $3x = 2x + 2R \implies x = 2R$ 5. $R = \frac{x}{2}$

Step 4: Final Answer:
To increase the range, connect a resistor of \( \frac{x}{2} \) $\Omega$ in series with the voltmeter.