Question

A 197 Ω resistor, a 0.925 H inductor, and a 5.75 μF capacitor are connected in series across a voltage source that has voltage amplitude 31.5 V and an angular frequency of 230 rad/s. What is v at t= 19.0 ms? What is vR at t= 19.0 ms? What is vL at t= 19.0 ms? What is  vC at t= 19.0 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

resistance, R=197 ohms

inductance, L=0.925 H

capacitance, C=5.75*10^-6 F

source voltage, Vo=31.5 v

angular frquency, w=230 rad/sec

and

inductive reactance, XL=w*L

XL=230*0.925 =212.75 ohms

capacitive reactance, XC=1/w*C

XC=1/(230*5.75*10^-6)=756.14

impedance Z=sqrt(R^2+(XL-XC)^2)

Z=sqrt(197^2+(212.75-756.14)^2)

Z=577.99 ohms

Z=578 ohms

current, I=Vo/Z

I=31.5/578=54.5*10^-3 A =54.5 mA

a)

now,

at time, t=19sec

vR=I*R*sin(W*t)

VR=(54.5*10^-3)*197*sin(230*19)

vR=8.22 v ----->

VC=I*XC*sin(wt-pi/2)

VC=(54.5*10^-3)*756.14*sin(230*19-pi/2)

VC=30.83 v ---->

VL=I*XL*sin(wt+pi/2)

VL=(54.5*10^-3)*212.75*sin(230*19+pi/2)

VL=9.08 v ----->

here,

Vo=31.5 v

and

(VR+VC+VL)=8.22+30.83+9.08

=48.13

and

Vo/((VR+VC+VL)=31.5/48.13

=0.65

b)

vR=I*R

VR=(54.5*10^-3)*197

vR=10.74 v ----->

VC=I*XC

VC=(54.5*10^-3)*756.14

VC=41.21v ---->

VL=I*XL*

VL=(54.5*10^-3)*212.75

VL=11.6 v ----->

here,

Vo=31.5 v

and

(VR+VC+VL)=10.74+41.21+11.6

=63.55 v

and

Vo/((VR+VC+VL)=31.5/63.55

=0.5