Tuesday, September 11, 2012

Norton's theorem solved problems(3)

Q4) In order to find the V1 & R1 values in the circuit shown in Figure14.12, power dissipation at the variable resistor Rload is measured, for the different values of Rload. The maximum power dissipated at Rload is measured as 81mW when the resistance R is set to 9kΩ. Find V1 & R1.

You have to solve this problem from the end to beginning. This means we must go backward in the problem.

As the problem says, the maximum power output occurs when RLOAD = 9kΩ. Therefore according to the maximum power transfer theorem, internal resistance as seen from A-B terminals is also equal to 9kΩ. So this resistance is therefore equal to the Norton’s resistance of A-B terminals.
As the maximum power dissipation at RLOAD = 9kΩ is equal to 81mW, we can find the current flowing through the load resistance RLOAD .

P = I2R

81mW = I2 X 9KΩ

I2 = 9 X 10-6

I = 3mA

So now we can draw the Norton’s equivalent circuit as shown is figure 14.12.a to determine the Norton’s current.

We can simply understand the Norton’s current is equal to 6mA, as the two resistance are equal and parallel connected.

Now we know the Norton’s current.

So now see figure 14.13.

As the Norton’s resistance is equal to 9kΩ, we can obtain the value of R1 now.

(R1//12kΩ) + 5kΩ = 9kΩ

R1//12KΩ = 4KΩ

R1 = 6KΩ

Now, we are about to draw the figure that we draw when we wants to find the Norton’s current. Of course we know the Norton’s value. But here we draw it to find V1. See figure 14.14

So as we know the value of IN, we can find the voltage across 5kΩ which is equal to the voltage at point c (V).

Ohm’s law to 5kΩ resistor,

V = IR

V = 6mA x 5kΩ

V = 30V

Now by applying nodal equation on point C,

V/12kΩ  + (V-V1)/6kΩ + 6mA = 0

30/12kΩ + (30-V1)/6kΩ + 6mA = 0

30/12kΩ + 30/6kΩ + 6mA = V1/6kΩ

V1 = 81V

If you have any problem please leave a comment.

Pabindu lakshitha
B.Sc (Engineering Undergraduate)


  1. In fig 14.12 a how did you determine resistance in the middle branch and the total current?
    It could also be 4.8A and 15ohm.

    1. Question says : The maximum power dissipated at Rload is measured as 81mW when the resistance R is set to 9kΩ....
      According to maximum power transfer theorem, internal resistance = load (at maximum power)
      So 14.12a shows that circuit.
      NOTE: that is not related to 14.12. figue 14.12a shows the equivalent circuit for a circuit which dissipate maximum power for 9ohms load


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