Example 10.5

1ECE 201 Circuit Theory 1

A load having an impedance of 39 + j26 Ω is fed from a voltage source through a line having an impedance of 1 + j4 Ω. The effective, or rms, value of the source voltage is 250 V.

Calculate the load current IL and the voltage VL.

2ECE 201 Circuit Theory 1

Calculate the load current IL and the voltage VL.

The line and load impedances are in series across the voltage source, so the load current equals the voltage divided by the total impedance. The load voltage equals the load current multiplied by the load impedance.

VV

IjZIV

Aj

I

L

LLLL

L

18.335.234

)87.365)(69.3387.46()2639(

87.36587.3650

0250

3040

0250

3ECE 201 Circuit Theory 1

Calculate the active and reactive power delivered to the load.

VAjS

S

S

jjIVS LL

650975

69.338.1171

)87.365)(18.336.234(

)34)(13234(*

Average Power = 975 W Reactive Power = 650 VARS

4ECE 201 Circuit Theory 1

Calculate the average and reactive power delivered to the line.

VARQ

XIQ

WP

RIP

eff

eff

100)4()5(

25)1()5(

2

2

2

2

Reactive Power is positive due to an inductive line reactance

5ECE 201 Circuit Theory 1

Calculate the average and reactive power supplied by the source

Add complex powers delivered to the line and load

VAjS

jjS

7501000

65097510025

6ECE 201 Circuit Theory 1

Calculate the apparent power**effeffeffeff IVIVS

The – sign is used whenever the current reference is in the direction of a voltage rise

VAjjSS )7501000()34(250

**effeffeffeffS IVIVS

7ECE 201 Circuit Theory 1