You have a 200 Ω resistor, a 0.400 H inductor, a 6.00 μF capacitor and a volta

Question

You have a 200 Ω resistor, a 0.400 H inductor, a 6.00 μF capacitor and a voltage source that has a voltage amplitude of 30.0 V and an angular frequency of 250 rad/s. The resistor, inductor, capacitor, and voltage source are connected to form an L-R-C series circuit. The current is given by i=Icos(ωt), so v=Vcos (ωt φ). What is v at t = 20ms? What is vR at t = 20ms? What is vC at t = 20ms? What is vL at t = 20ms? What is v at t = 40ms? What is vR at t = 40ms? What is vC at t = 40ms? What is vL at t = 40ms?

Explanation / Answer

voltage v=30cos(wt+p)

voltage across resistor is same as voltage of source

v=Vr= 30coswt

v at 20ms t=0.020 s

v=30cos(250*0.020)=8.50

Vr at 20ms is also Vr=8.50 v

v at 40 ms

v = Vr = -25.17 V

Voltage across capacitor

Vc=30cos(wt-pi/2)

at t =20 ms=0.020 sec

Vc =30cos(250*0.020-3.14/2) =-28.76

Vc at 40 ms Vc=-16.34 V

voltage across inductor

VL=30cos(wt+pi/2)

at t=20ms=0.020 s

VL=+28.76 V

at t=40ms=0.040 s

VL=+16.34 V

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