Question

(HW11-31.14) You have a 230-? resistor and a 0.380-H inductor. Suppose you take the resistor and inductor and make a series circuit with a voltage source that has a voltage amplitude of 26.0 V and an angular frequency of 300 rad/s .

A) What is the impedance of the circuit?

B) What is the current amplitude?

C) What is the voltage amplitude across the resistor?

D) What is the voltage amplitudes across the inductor?

E) What is the phase angle ? of the source voltage with respect to the current?

G) Construct the phasor diagram.

Draw the phasors starting at the black dot. The location and orientation of the phasors will be graded. The length of the phasors will not be graded.

Answer 1

Ans :

Given R = 230?; L = 0.41H; Voltage amplitude E =26 V

? = 300 rad/s

a.

Z = Sqrt ( R² + (X_C –X_L)²)

Z = sqrt ( R² + (?L)²)

Z = sqrt ((230)² + (300 x 0.41)²)

Z = sqrt(52900+15129)

Z = 260.8 ?

b.

I = E/ Z

I = 26/260.8

I = 0.0996A

c.

V_R = IR = 0.0996 x230

V_R = 22.91V

d.

V_L = IX_L

X_L = L = 300 x 0.41 = 123

= 0.0996 x 123

V_L = 12.51V

e.

? = tan ^–1 (X_L/R)

? = tan ^–1 (123/230)

? = 28^O       (please check the calculation)

f.