Question

An inductive coil connected to a 200 V, 50 Hz AC supply with 10 A current flowing through it dissipates 1000 W. The value of the impedance Z and Reactance XL are respectively ____________

(a) 10 Ω and 15 Ω

(b) 20 Ω and 17.3 Ω

(c) 17.3 Ω and 20 Ω

(d) 15 Ω and 10 Ω

I had been asked this question in an international level competition.

The doubt is 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 (b) 20 Ω and 17.3 Ω

Easy explanation: Power dissipated is given by,

I^2R = 1000 W

Hence, R = \(\frac{1000}{100}\)

Or, R = 10 Ω

Impedance Z = \(\frac{V}{I} = \frac{200}{10}\)

Or, Z = 20 Ω

Reactance XL = \(\sqrt{Z^2 – R^2}\)

= \(\sqrt{20^2 – 10^2}\)

∴ XL = 17.3 Ω.