Question

A series circuit of a 45 Ω resistor, a 2.5 H inductor, and a 36 µF capacitor is connected to source that the emf is given by e = 340 cos(628t-50).

A.Find the sinusoidal expression of the total current.

B.The r.m.s values of the source voltage and the total current

C. The power dissipated in the circuit and the power factor of the circuit.

Answer 1

from voltage eqn w = 628 rad/s |V| = 340 V (peak voltage)
your complex z = 45 + j(w * 2.5 - 1/(w*36*10^-6)) = |z| angle ( atan(imag/real) ) = |z| |_ Theta

expresn for peak current = |I| = |V|/|Z| = 340 / |Z|

rms voltage = 340/sqrt(2)
rms current = peak current / sqrt(2)

angle of current = angle(V) - angle(Z) = -50 - angle(Z)

so I = |I| cos(628t - angle of current)

power = VI* = rms voltage * rms current * cos(angle of voltage - angle of current) Watts