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Equivalent Voltmeter and Ammeter

Two 100 V ful...

Question

Two 100 V full scale PMMC type dc voltmeter having figure of merits (FOM) of $10 k Ω / V$ and $20 k Ω / V$ are connected in series. The series combination can be used to measure a maximum DC voltage of ____V.
150

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Solution

The correct option is A 150
$(I_{f s d})_{1} = \frac{1}{10 k Ω / V} = 0.1 m A$
$(I_{f s d})_{2} = \frac{1}{20 k Ω / V} = 0.05 m A$
In series application, maximum current will be 0.05 mA.

$R e s i s t a n c e o f M_{1} = 10 k Ω / V \times 100 V = 1 M Ω$

$R e s i s t a n c e o f M_{2} = 20 k Ω / V \times 100 V = 2 M Ω$

Hence, the maximum voltage rating

$= I_{m a x} . (R_{M_{1}} + R_{M_{2}})$

$= 0.05 m A \times (1 + 2) M Ω = 150 V$

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