Question

An ac voltage \(V = 280 \sin (100\pi t)\) volt is connected across a series LCR circuit in which \(R = 400 \, \Omega\), \(L = \frac{5}{\pi} \, \text{H}\) and \(C = \frac{50}{\pi} \, \mu\text{F}\). Taking \(\sqrt{2} = 1.4\), calculate :
(I) impedance of the circuit.
(II) rms value of current that flows in the circuit.
(III) power factor of the circuit.

Hint:

Whenever you encounter values like 300 and 400 for orthogonal components, remember the standard Pythagorean triplet (3, 4, 5). Here, \(\sqrt{400^2 + 300^2}\) instantly reveals itself to be 500, reducing calculation errors significantly during tests!

Answer 1