Analog meter sensitivity: For a 30,000 Ω/volt voltmeter set to its 50 V range, what is the instrument's internal resistance (use sensitivity × full-scale voltage)?

Introduction / Context:
Traditional analog voltmeters are often specified by their sensitivity in ohms per volt (Ω/V). This figure tells you how much internal resistance the meter presents for each volt of full-scale deflection. Understanding this is essential when estimating meter loading effects on the circuit under test.

Given Data / Assumptions:

• Sensitivity (meter constant): 30,000 Ω/V.
• Selected meter range: 50 V.
• We assume an ideal analog meter movement where R_internal = sensitivity × full-scale voltage.

Concept / Approach:

The internal resistance of an analog voltmeter on a given range equals the product of its Ω/V sensitivity and the full-scale range setting. This arises because the range switch inserts series resistance so that the meter movement sees its required current at full scale while presenting the specified resistance to the circuit.

Step-by-Step Solution:

Verification / Alternative check:

If the meter were set to a different range, internal resistance would scale proportionally. For example, at 10 V it would be 300 kΩ; at 100 V it would be 3 MΩ. This linear scaling confirms the formula's consistency.

Why Other Options Are Wrong:

15,000 Ω and 150,000 Ω are smaller by factors of 100 and 10 respectively. 15,000,000 Ω corresponds to 300,000 Ω/V on 50 V—far above the stated sensitivity.

Common Pitfalls:

Confusing the Ω/V rating with the total resistance; forgetting to multiply by the selected range; misreading units (kΩ vs MΩ).

Final Answer:

1,500,000 Ω