Question

In the circuit shown below, ta) Find the value of R. b) Find the angular l requency a) ofthe current source. 10 mF

Answer 1

Given circuit is i(t) = 10 squareroot 2 cos (wt + 60^dot) = 10 squareroot 2 llcorner 60^dot v (t) = 100 cos (wt + 15^dot) = 100 llcorner 15^dot Find 'R' we know v(t)/i(t) = Z Z = impendence = 100 llcorner 15^dot/10 squareroot llcorner 60^dot = 7.07 llcorner -45^dot = 10/ squareroot 2 llcorner -45^dot As R and C are in parallel: 1/Z = 1/R + 1/(1/jwc) = > 1/Z = 1/R + jwc = > squareroot 2/10 llcorner 45^dor = 1/R + jwc = > squareroot 2/10 cos 45^dot + j squareroot 2/10 sin 45^dot = 1/R + jwc = > squareroot 2/10 (1/ squareroot 2) + j squareroot 2/10 (1/ squareroot 2) = 1/R + jwc comparing real parts both sides 1/R = 1/10 = > R = 10 Ohm comparing imaginary parts: wc = 1/10 = >