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Homework Statement
In the circuit shown, a load having an impedance of 39 + j26Ω is fed from a voltage source through a line having an impedance of 1 + j4Ω. The rms value of the source voltage is 250V.
a) Calculate the load current IL and voltage VL
b) Calculate the average and reactive power delivered to the load
Homework Equations
V = IR
I = V/R
voltage division
Polar form conversion
j*j = -1
1/j = -javerage power = VIcos∅
cos∅ = power factor
calculating power factorreactive power = (apparent power)sinθ
The Attempt at a Solution
Simplify to this first:
and then voltage division:
VL = (250∠0 deg)*[ (39Ω + 26Ωj)/(40Ω + 30Ωj) ] and in complete polar form:
VL = (250∠0 deg)*[ (46.8∠33.6)/(50∠36.8) ] VL = (234∠-3.25)Vsince the drop VL on the diagram is in the opposite direction thoughVL = (-234∠-3.25)VIL = (250∠0 V) / (50∠36.8 Ω)
IL = 5∠-36.8 ANow, not sure how to get part b from here. Any hints on how to calculate the angle to get power factor? What is meant by the angle between voltage and current to get power factor (and then being able to find average power)?
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