A series RLC circuit s observed at two frequencies. At ω1

A series RLC circuit s observed at two frequencies. At ω₁ = 1 k rad/s, we note that source voltage V₁ = 100 ∠0°V results in current I₁ = 0.03 ∠31° A. At ω₂ = 2 krad/s, the source volt age V₂ = 100 ∠0° V results in a current I₂ = 2 ∠0° A. The closest values for R, L, C out of the following options are

1. R = 50 Ω ; L = 25mH ; C =10μF;
2. R = 50 Ω ; L =10mH ; C = 25μF;
3. R = 50 Ω ; L = 50mH ; C = 5μF;
4. R = 50 Ω ; L = 5mH ; C = 50μF;

at ω₂ = 2000 r/sec

φ = 31° ⇒ tan^-1		X_L - X_C
		R

⇒ tan31° =		X_L - X_C
		R

⇒		ω₁L -	1		= 0.600 × 50
			ω₁C

⇒		ω₁L -	1		= 30.04 q ......(1)
			ω₁C

⇒	ω₂L -	1	= 0 ......(2)
		ω₂C

ω₁ = 1000 r / sec ;
ω₂ = 2000 r / sec
from 1 and 2, C = 25 μF
L = 10 mH