Choosing an appropriate voltmeter: which instrument specification minimizes loading when measuring the voltage across a 20 kΩ resistor?

Introduction / Context:
When measuring voltage across a component, the voltmeter should draw negligible current so that the circuit under test is not disturbed. Sensitivity in kΩ/V (for analog meters) indicates the input resistance per volt of range; higher sensitivity means higher input resistance and less loading.

Given Data / Assumptions:

• Measured element: 20 kΩ resistor.
• Analog voltmeters characterized by sensitivity (kΩ/V).
• We seek the highest practical input resistance compared with 20 kΩ.

Concept / Approach:

Loading error is minimized when R_meter ≫ R_load. For a sensitivity S (kΩ/V) on a V-range, R_meter = S * V (in kΩ). A 10 kΩ/V meter on, say, a 10 V range has 100 kΩ input—five times the 20 kΩ load—resulting in reasonable accuracy compared to a 1 kΩ/V meter (only 10 kΩ on 10 V range) or a fixed 5 kΩ instrument.

Step-by-Step Solution:

Verification / Alternative check:

Digital voltmeters typically have 10 MΩ input, giving negligible loading; among the given analog choices, 10 kΩ/V is the best to reduce error.

Why Other Options Are Wrong:

• 5 kΩ and 1 kΩ/V lead to substantial current draw and large measurement error.
• Equal to 20 kΩ still causes 50% voltage division error.
• “None” is incorrect because a suitable option exists.

Common Pitfalls:

• Ignoring how sensitivity and selected range determine input resistance.

Final Answer:

Voltmeter with sensitivity of 10 kΩ/V