Question

A rectifier type AC voltmeter consists of a series resistance R, an ideal full-wave rectifier bridge and a PMMC instrument. A DC current of 1 mA produces a full-scale deflection of the instrument. The resistance of the instrument is 100 Ω. A voltage of 100 V (rms) is applied to the input terminals. The value of R required is?

(a) 63.56 Ω

(b) 89.83 Ω

(c) 89.83 kΩ

(d) 141.3 kΩ

I had been asked this question by my college professor while I was bunking the class.

Question is taken from Problems Involving Standard Time Functions in division Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

The correct choice is (c) 89.83 kΩ

The explanation: VOAverage = 0.636 × \(\sqrt{2}\)Vrms = 0.8993 Vrms

The deflection with AC is 0.8993 times that with DC for the same value of voltage V

SAC = 0.8993 SDC

SDC of a rectifier type instrument is \(\frac{1}{I_{fs}}\) where Ifs is the current required to produce full scale deflection, Ifs = 1 mA; Rm = 100 Ω; SDC = 10^3 Ω/V

SAC = 0.8993 × 1000 = 899.3 Ω/V. Resistance of multiplier RS = SAC V – Rm – 2Rd, where Rd is the resistance of diode, for ideal diode Rd = 0

∴ RS = 899.3 × 100 – 100 = 89.83 kΩ.