Voltmeter conversion design: A 100 Ω, 1 mA full-scale movement must be converted to a 0–5 V DC voltmeter. Determine the value of the series multiplier resistor to be added.

Introduction / Context:
Analog voltmeters are created by adding a series multiplier to a sensitive moving-coil (PMMC) movement. The series resistor limits current so that full-scale deflection occurs at the desired terminal voltage. This problem practices the direct sizing of that multiplier.

Given Data / Assumptions:

• Meter internal resistance Rm = 100 Ω.
• Full-scale meter current Im = 1 mA = 0.001 A.
• Desired range Vfs = 5 V.

Concept / Approach:

At full scale, terminal voltage equals voltage drop across the series resistor plus the internal drop across the movement. Use Ohm’s law to calculate the required series resistor so that total drop equals the target range.

Step-by-Step Solution:

Verification / Alternative check:

Check: At 5 V the current is 5 / (4900 + 100) = 5 / 5000 = 1 mA → full-scale; at lower voltages the deflection is proportional, as expected for a PMMC voltmeter in DC.

Why Other Options Are Wrong:

• 490 Ω / 5100 Ω / 4500 Ω: do not yield 1 mA at 5 V.
• 5000 Ω: ignores the movement’s internal 100 Ω.

Common Pitfalls:

• Forgetting to subtract the meter resistance from the total resistance required.
• Confusing mA with A when computing R_total.

Final Answer:

4900 Ω