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I have to find the power in the 4-ohm resistor in the circuit below.

In mesh 1 we have: \$16\angle 0 \mathrm V = 2I_1 - 8I_3 + V_1\$

In mesh 2 we have: \$V_2 = 4I_2\$

In mesh 3 we have: \$0 = 10I_3 - 2I_1\$

\$5I_3 = I_1\$

By the circuit we notice that \$V_2 = 2V_1\$ and \$I_1=2I_2\$.

Here I find \$I_2\$ So I can find \$P = 0.5*I_2^2 * 4\Omega\$ but the problem is that in my book \$P = 18 \mathrm W\$, which isn't the result I get. Where is my mistake?

Circuit schematic showing mesh currents

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3 Answers 3

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This sounds like a school question. So I'm going to give only hints.

1) what is the RMS voltage?

2) Assuming that the voltage source is perfect (zero source impedance), what does that voltage source look like at the secondary winding of the transformer. In other words, you can easily calculate both the voltage and the effective source impedance given the information in your diagram.

3) Is the voltage at the secondary of the transformer in phase with the primary?

4) Use all of the above information and then add in the effect of the 8 Ohm resistor.

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Your loop 3 seems to punch the transformer at the top edge which is nonsense. No such conductive path exists. Fix it easily by changing loop 3 to go through the 4 Ohm resistor.

Another solution:

Assume unknown transformer voltage Uout over the 4 Ohm resistor and unknown Iout from the transformer to the 4 Ohm resistor.

You can write 2 equations from the circuit loops

1) The input source voltage (16/sqrt(2)) volts = the sum of the voltages over 8 Ohm and 4 Ohm resistors. The latter is Uout.

2) As well (16/sqrt(2)) volts = the sum of the voltage over the 2 Ohm resistor and the primary voltage of the transformer. Use current 2*Iout for the 2 Ohm resistor and use voltage Uout/2 to be present in the primary of the transformer.

Eliminate Iout and solve Uout. The calculated power to the 4 Ohm resistor is 18 watts as claimed.

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There are a couple of mistakes in your analysis:

Mesh 1 should be 16=2(I1-I3)+V1

Mesh 3 should be V1-V2=10I3-2I1.

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