Question

A 202 Ω resistor, a 0.950 H inductor, and a 5.00 μF capacitor are connected in series across a voltage source that has voltage amplitude 30.0 Vand an angular frequency of 260 rad/s .

Part A

What is v at t= 19.5 ms ?

Part B

What is vR at t= 19.5 ms ?

Part C

What is vL at t= 19.5 ms ?

Part D

What is vC at t= 19.5 ms ?

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?

Answer 1

A)

$Volatage\at\ t=19.5ms, v\ given \ as \ V(t) = V Sin \omega t \\\ v= 30Sin (260*19.5*10^{-3}) = 13.62Volts$

B)

$Impedence Z = R+X_L+X_C=R \hat{i} +\omega L\hat{j}-\frac{1}{\omega C}\hat{j}\\ Z=\sqrt{202^2+(247-769.2)^2}=560\angle -68.85 \\\\ I = \frac{V}{Z}=13.62/(560\angle -68.85) = 24.32mA\angle 68.85\\\\ Part B) \Rightarrow vR = I * R = 24.32mA\angle 68.85* 202=4.912\angle 68.85\\\\$

$Part C) \Rightarrow vL = I * X_L = 24.3mA\angle 68.85* 247\angle 90=6.007\angle 158.85\\$

$Part D) \Rightarrow vC = I * X_C = 24.3mA\angle 68.85* 769.2\angle -90=18.7\angle-21.2\\$

$Part E) \Rightarrow vC+vL+vR =13.6\hat{i}+0.0105\hat{j}\approx13.62 that\ is \ v\ in\ Part\ A$