UNIVERSITY OF MASSACHUSETTS DARTMOUTH
DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
ECE 201
CIRCUIT THEORY I
PRACTICE PROBLEM ON MAXIMUM POWER AND THEVENIN’S THEOREM
The variable resistor is adjusted for maximum power transfer to RL.
XWM1
V
R2
R4
4kΩ
1.25kΩ
RL
R3
10kΩ
I1
9mA
R1
2kΩ
10kΩ
50%
Key=A
V1
50 V
a) Find the value of RL.
The required value of RL will be the Thevenin equivalent resistance.
XMM1
R2
R4
4kΩ
R1
2kΩ
I
1.25kΩ
R3
10kΩ
(10k )(4k   2k )
10k   4k   2k 
RTh  1.25k   3.75k 
RTh  1.25k  
RTh  5k 
b) Find the maximum power that can be delivered to RL.
Determine the Thevenin voltage Vab.
Convert the 9 mA current source in parallel with the 2 kΩ resistor into an 18 V source in
series with the 2 kΩ resistor. Apply voltage division to find the voltage across the 10 kΩ
resistor and subtract that voltage from the 50 V source.
XMM1
R1
R2
2kΩ
4kΩ
R4
a
1.25kΩ
R3
10kΩ
V2
18 V
V1
50 V
b
10k 


V10 k   (50  18) 

 2k   4k   10k  
V10 k   20V
Vab  50  20  30V
The Thevenin equivalent circuit with the load connected is
RTh
5kΩ
VTh
30 V
RL
10kΩ
50%
Key=A
VL2 152
PL 

 45mW
RL 5k