Optimizing Power on a Resistor: Finding the Maximum Power

[crom1]

Homework Statement

Find the maximal power on resistor R.

Homework Equations

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The Attempt at a Solution

I used Thevenin theorem. I found that Z_t=5+j10 , and U_t= 10-j10. The maximum power happens in this case when $$R=|Z_t| = 5 \sqrt{5}$$ , and I get that P=6.18, while the answer is P=8.3.
Where did I went wrong?

 

[gneill]

There's hard to tell where you went wrong if you don't show the details of your work.

However, can you show how you found the Thevenin impedance?

 

[crom1]

When I look at it again, I get Z_t=5+j5,but I still get wrong solution. Do you want me to post my full (wrong) solution?

I found 5+j5 (parallel circuit of 10 ohms and j10 ohms)

 

[gneill]

When I look at it again, I get Z_t=5+5i,but I still get wrong solution. Do you want me to post my full (wrong) solution?

Yes, that would be best.

 

[crom1]

So I found thevenin impedance as parallel circuit of 10 ohms and j10 ohms (I can ignore 10 ohms and -j10 ohms since there is voltage source parallel to them).
Point A is to the left of our resistor , and point B to the right.
Bottom line of a circuit has potential equal to 0 (i don't know how to say it in english, hope you understand).
point A has potential 10V. When finding potential of point B, i ignore voltage source of 10V( the on the left). The impedance is parallel circuit of 10+j10 and 10-j10 so Z=10 ohms.
The current is then 1+j. The current going through 10+j10 is exactly 1 A, so the potential of B is j10. Now U_th= 10-j10.
R should be 5 sqrt(2) , the current in thevenin circuit should be I=U_th/(Z_th+R) = 1.083 (effective value) and power is P=I^2R=5.86

 

[gneill]

Your Thevenin impedance and voltage look good, as do the resistance and the magnitude of the current that you found. The first problem I can see is with the very last bit, the calculation of the power, P = I²R. Check that calculation again. Break it down by calculation step if necessary.

 

[crom1]

Thank you, I was putting R=5 this whole time and not 5sqrt(2). Now it's correct.