Question

A 217 Ω resistor, a 0.775 H inductor, and a 6.50 μF capacitor are connected in series across a voltage source that has voltage amplitude 31.5 Vand an angular frequency of 225 rad/s .

What is v at t= 19.5 ms ?

What is vR at t= 19.5 ms ?

What is vL at t= 19.5 ms ?

What is  vC at t= 19.5 ms ?

Compare vC+vL+vR and v at this instant:

What is VR?

What is VC?

What is VL?

Compare V and VL+VC+VR:

Answer 1

step;1

Given that

resistance R=217 ohm

inductor L=0.775 H

capacitance C=6.5*10^-6 F

angular frequency W=225 rad/s

step;2

now we find the voltage

V=31.5*sin(225*19.5*10^-3)=2.41 v

current I=2.41/[217^2+(225*0.775-1/225*6.5*10^-6)^2]^1/2

             =2.41/[217^2+(174.4-683.8)^2]^1/2

             =2.41/553.7

             =4.4 mA

voltage on resistance Vr=4.4*10^-3*217=0.9548 v

voltage on inductance VL=4.4*10^-3*225*0.775=0.77 v

voltage on capacitance Vc=4.4*10^-3*1/225*6.5*10^-6=3.01 v

V=VL+Vr+Vc=3.01+0.9548+0.77=4.7348 v