Question

A voltmeter has a sensitivity of 1000 Ω/V reads 200 V on its 300 V scale. When connected across an unknown resistor in series with a millimeter, it reads 10 mA. The error due to the loading effect of the voltmeter is

(a) 3.33%

(b) 6.67%

(c) 13.34%

(d) 13.67%

I got this question by my school teacher while I was bunking the class.

My doubt stems from Advanced Problems on Two Port Network topic in portion Two-Port Networks of Network Theory

Answer 1

The correct option is (b) 6.67%

The best explanation: RT = \(\frac{V_T}{I_T}\)

VT = 200 V,  IT = 10 A

So, RT = 20 kΩ

Resistance of voltmeter,

RV = 1000 × 300 = 300 kΩ

Voltmeter is in parallel with unknown resistor,

RX = \(\frac{R_T R_V}{R_T – R_V} = \frac{20 ×300}{280}\) = 21.43 kΩ

Percentage error = \(\frac{Actual-Apparent}{Actual}\) × 100

= \(\frac{21.43-20}{21.43}\) × 100 = 6.67%.