Question

A 193 Ω resistor, a 0.750 H inductor, and a 6.00 μF capacitor are connected in series across a voltage source that has voltage amplitude 28.5 V and an angular frequency of 245 rad/s . What is vR at t= 18.0 ms ? What is vL at t= 18.0 ms ? What is vC at t= 18.0 ms ?

Answer 1

Given that

The resistance (R) =193ohm

The inductor (L) =0.750H

The capacitor (C) =6.00uF =6*10^-6F

The voltage amplitude is (V) =28.5V

The angualr frequency is given by (w)= 245rad/s

Then we can assume that V =28.5sin(245t)

Now capacitive reactance is Xc =1/wc =1/245*6*10^-6F =680ohm

                                         XL =wL (245)(0.750H)=183.75=184ohm

The resistance (R) =193ohm

Now the total imepdance of the circuit is given by Z =Sqrt(R²+(XL-Xc)² =Sqrt(37249+246016)=532.226ohm

Now the total current flowing through the circuit is

V =I*Z

Then I =V/Z =28.5/532.226 =0.0535A

Then we can assume that V =28.5sin(245t) at 18ms

v =28.5sin(245*18*10-3) =2.1914V

The current at this particular time is I =V/Z =2.1914/532.226 =4.11mA

Now VR =(4.11mA)()

Now VR =I*R =(0.0535A)(193) =10.325V

        VL =I*XL =(0.0535A)(184ohm)=9.844V

        Vc =I*XC =(0.0535A)(680) =36.38V