Question

A 211 ? resistor, a 0.775 H inductor, and a 5.50 ?F capacitor are connected in series across a voltage source that has voltage amplitude 30.0 V and an angular frequency of 230 rad/s

PART A What is v at t= 21.0 ms ?

Express your answer with the appropriate units.

PART B

What is vR at t= 21.0 ms ?

Express your answer with the appropriate units.

PART C

What is vL at t= 21.0 ms ?

Express your answer with the appropriate units.

PART D

What is vC at t= 21.0 ms ?

Express your answer with the appropriate units.

PART E

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

PART F

What is VR?

PART G

What is VC?

PART H

What is VL?

PART I

Compare V and VL+VC+VR:

Answer 1

Please do not post these many parts at once

I will solve first four subparts only as per the rules

X_L = wL = 230*0.775 = 178.25 ohms

X_c = 1/wC = 1/ 230*5.50e-6 = 790.5 ohms

phi = tan^-1 (X_L - X_c / R)

phi = tan^-1 (178.25 - 790.5 / 211)

phi = tan^-1 ( - 2.901658)

phi = - 1.2389

Z = sqrt (R² + (X_L - X_c )²

Z = 647.59 ohms

I = V/Z = 30 / 647.59 = 0.046325 AMPS

(a) V at t = 21 ms

V = 30 cos(230*21e-3 - 1.2389)

V = - 27.0198 volts

(b) V_R = IR cos (wt)

V_R = 0.046325*211 cos (230*0.021)

V_R = 1.1469 v

(c) V_L = IX_L COS (wt + pi / 2)

V_L = 8.2 V

(d) V_c =  IX_c COS (wt - pi / 2)

Vc = - 36.367 V