Question

You have a 220 Ohm resistor, a 0.400 H inductor, and a 7.00 mu F capacitor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has voltage amplitude 30.0 V and an angular frequency of 250 rad/s. (a) What is the impedance of the circuit? Ohm (b) What is the current amplitude? A (c) What are the voltage amplitudes across the resistor and across the inductor? V (across the resistor) V (across the inductor) (d) What is the phase angle phi of the source voltage with respect to the current? (Include the sign of the value in your answer.) Does the source voltage lag or lead the current? leads lags (e) Construct the phasor diagram. (Submit a file with a maximum size of 1 MB.)

Answer 1

a)

R = 220 ohm

L = 0.4 H

w = 250 rad/s

X_L = inductive reactance = wL = 250 x 0.4 = 100 ohm

impedence is given as

z = sqrt(R² + X_L²) = sqrt((220)² + (100)²) = 241.7 ohm

b)

i = V/z = 30/241.7 = 0.124 ohm

c)

V_r = Voltage across resistor = i R = (0.124) (220) = 27.3 volts

V_in = Voltage across inductor = i X_L = (0.124) (100) = 12.4 volts

d)

tan $\phi$ = X_L/R = 100/220

$\phi$ = tan^-1(100/220) = 24.44 degree

Voltage leads the current