Question

To minimize loading, the voltmeter should have:

• A. Low Resistance
• B. High Resistance
• C. High Current
• D. Low Voltage

Hint:

Voltmeter \( \implies \) Connected in Parallel \( \implies \) Ideal Resistance \( = \infty \) (High Resistance).
Ammeter \( \implies \) Connected in Series \( \implies \) Ideal Resistance \( = 0 \) (Low Resistance).

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks what physical property a voltmeter must possess to minimize the "loading effect" on the circuit where the voltage is being measured.
Loading effect is a major source of systematic error in electrical measurements.

Step 2: Key Formula or Approach:
A voltmeter is always connected in parallel across the two points in a circuit whose potential difference is to be determined.
Let the circuit have an equivalent resistance of \( R_{\text{th}} \). When the voltmeter with internal resistance \( R_v \) is connected, the parallel combination becomes:
\[ R_{\text{eq}} = \frac{R_{\text{th}} \cdot R_v}{R_{\text{th}} + R_v} \] To ensure that the circuit's original state is not disturbed, we require \( R_{\text{eq}} \approx R_{\text{th}} \). This is only possible if \( R_v \gg R_{\text{th}} \).

Step 3: Detailed Explanation:
Let us explore the impact of voltmeter resistance on the measurement error:

• Ideal Case: An ideal voltmeter must draw zero current from the test circuit. According to Ohm's Law:
\[ I_v = \frac{V}{R_v} \] For \( I_v \) to be exactly zero, \( R_v \) must be infinite (\( \infty \)).

• Practical Loading Error: If a voltmeter with low resistance is connected across a high-resistance component, it creates a parallel bypass path.
This causes a significant drop in the equivalent resistance of that branch, drawing a large shunt current away from the circuit.
As a result, the voltage measured across the parallel branch drops significantly below the true open-circuit voltage. This drop is the loading error.

• Prevention: To minimize this loading error, voltmeters are engineered to have as high an internal resistance (\( R_v \)) as possible.

Step 4: Final Answer:
To minimize loading, practical voltmeters must possess a very high resistance.