Question

P5 [Ex. 9.60) Use the mesh-curren at method to find the steady-state expression for i.(t) in the circuit below, if valt) -100 cos 50000t V, and t)-100 sin(50000t+ 180°) v.

Answer 1

Transforming the circuit into phasor domain V_a (t) = 100 cos 50000 t V_a = 100 angle 0 degree V_b (t) = 100 sin (50,000 t + 180 degree) = 100 sin (50,000 t + 90 degree + 90 degree) = 100 cos (50,000 t + 90 degree) V_b = 100 angle 90 degree L = 100 mu H rightarrow j omega L = j times 50,000 times 100 times 10^-6 = j5 c = 2 mu rightarrow -j/omega c = -j times 1/50,000 times 2 times 10^-6 = -j10 Now, applying KVL in loop I, -100 angle 0 degree + 10i_1 + j5 (i_1 - i_2) = 0 rightarrow 10i_1 + j5 i_1 - j5 i_2 = 100 rightwardsdoublearrow (10 + j5) i_1 - j5 i_2 = 100____(i) \r\n Applying KVL in loop II, -j10 i_2 - 100 angle 90 degree + j5 (i_2 - i_1) = 0 rightarrow -j5 i_1 - j10 i_2 + j5 i_2 = 100 angle 90 degree rightarrow -j5 i_1 - j5 i_2 = 100 angle 90 degree___(ii)
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