- #1
timeforplanb
- 17
- 0
Homework Statement
Determine the value of RL that will draw the maximum power from
the rest of the circuit shown below. Calculate the maximum power. (This problem was included in our exam this week, and I don't really recall the exact values of the parameters, but I'm pretty sure that the circuit looks more or less like this.)
Homework Equations
V=IR
P=I2R
KVL
The Attempt at a Solution
Computing for Vab:
mesh 1:
-10+5I1+15(I1-I3)=0
but I3=0, so I1=2A
mesh 2:
I2=3Vx
but Vx=-6I3, and I3=0, so I2=0
Since no voltage exists in the 3 and 6 ohm resistors, I shorted them and Vab will now be equal to the voltage across the 15 ohm resistor. (Will it? I'm not really sure about this)
Therefore,
V5ohm=Vab=15I1=15(2)
Vab=30V
Computing for Rab:
mesh 1:
20I1-153=0 --> eqn.1
mesh 2:
I2=3Vx
but Vx=-6I3
I2=3(-6I3)
I2+18I3=0 --> eqn.2
mesh 3:
-15I1-3I2+24I3=0 --> eqn. 3
I1=-0.011A
I2=0.270A
I3=-0.015A
I=-I3=-(-0.015)
I=0.015A
Rab=1/I=1/0.015
Rab=66.667ohms
Computing for the maximum power:
Pmax=I2Rab=(30/(66.667+66.667))2(66.667)
Pmax=3.375W
That is what I did. Sirs, did I solve it the right way? I'm especially uncertain about how I solved Vab.
Attachments
Last edited: