The two elements in the circuit given below are,
v(t) = 50 cos(5000t + 30°) V
i(t) = 10 cos (5000t - 23.13°) A
∴ The elements will be R and L
tanϕ=ωLR
tan(53.13∘)=1.33=5000LR...(i)
[Since ω = 5000 rad/sec]
VI=|Z|=5010=√R2+(ωL)2
5=√R2+(ωL)2
25=R2+(5000L)2
From equation (i), ... (ii)
L=R×1.335000
25=R2+(1.33R)2
R=3Ω
Substituting in equation (ii), we get
L=3×1.335000=0.8mH