# AC circuit, mystery impedance

• Engineering

## Homework Statement

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a) Write an expression for V1 and V2 both in time domain and phasor domain (Solved)

b) Write an expression for the current I both in time domain and phasor domain (Solved)
c) Calculate the Power factor of the supply and specify whether it is lagging or
d) Specify the type of the reactance (XC or XL)
e) Determine the value of X and hence the corresponding value of L or C
f) Calculate the supply average, reactive and apparent power
g) Draw the phasor diagram of the circuit

f= 250/3

## The Attempt at a Solution

a)
V1 = 10sqrt(2)<48 = 9.46+10.51
V2 = 5/sqrt(2)<0 = 3.54
b)
I = v2/r2 = 0.354<0
c)
PF = 0.669, lagging
d)

X is an inductor

e)
VCh2 + Vxl = Vsource
Vxl = 9.46+10.51j - 5/sqrt(2) = 5.93 +10.51j = 12.1<60.6

Zx = Vxl/Is = 12.1<60.6 / 0.354<0 = 16.77+ 29.73j

This tells me that there's a physical impedance associated with the coil, equal in value to 16.77ohms...Meaning that it's not a pure inductor?

To find L:

29.73 = 2*pi*f*L ... 29.73/ (2*pi*250/3) = L = 0.057H

But these results don't add up to the next few parts:

-Active Power-
P(10ohm)=I^2*R=(0.354)^2*10 = 1.25W
P(16.77ohm)=I^2*R=(0.354)^2*16.77 = 2.10W
Total:3.35W

-Reactive Power-
P(XL)=I^2*R=(0.354)^2*29.73 = 3.72VAR

-Apparent Power-
Active+Reactive*j = 3.35+3.72j

which matches:

S=EI=10sqrt(2)<48 * 0.354<0 = 3.35 + 3.72j

Have I done this question correctly? Is it possible that the inductor has a simple resistance component to it?

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