Question

The pf of a load is measured by measuring voltage, current and power. The nominal values are 10 V, 1 A and 8 W respectively. The limiting errors in the readings of voltmeter, ammeter and wattmeter are ±2 %, ±3 % and ±4 % respectively. The limiting error in the measurement of pf is
1. ±2.38%
2. ±5.23%
3. ±10.5%
4. ±9%

Answer 1

Correct Answer - Option 4 : ±9%

Concept:

Limiting error:

• The maximum allowable error in the measurement is specified in terms of true value, is known as limiting error.
• It will give a range of errors. It is always with respect to the true value, so it is a variable error.
• If two quantities are getting added, then their limiting errors also gets added.
• If two quantities are getting multiplied or divided, then their percentage limiting errors gets added.

Calculation:

Given that, P = 8 W ± 4%

V = 10 V ± 2%

I = 1 A ± 3%

P = VI cos ϕ

Power factor (cos ϕ) = P/VI

Limiting error in the measurement of power factor is

= ± 2 ± 3 ± 4 = ±9%