Homework Help: Maximum power transfer and kirchoffs

1. Apr 14, 2013

Andrew187

Hi Folks
I need a bit of help, My weakness is kirchoffs law and algebra, I know but I still give it a try. For this task I am required to calculate the value of the load (RL) using kirchoffs and then I have to find the maximum power transfer for the circuit. I have attempted to calculate the load (RL) using kirchoff now the bit that I am confused on is am I looking for the resistance of the Load (RL) or the current in the load (RL). Which figure is required to calculate the maximum power transfer? is it the current or resistance of the load (RL)? If it is the current is my calculations correct? and if its the resistance I need to calculate, how do I figure that out because I have no clue where to start:(

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2. Apr 14, 2013

Staff: Mentor

The value that you found for I2 is okay. Things go off the rails when you get to the section "Sub I2 in to equation (1). You write:
$$I_1 = 15v + \frac{0.293a}{15v} = 15.02$$
which doesn't make sense. The units are not consistent; current is not the same as voltage. Later you have RL = 15.03a, but RL is a resistance, not a current.

Can you state the "Max Power theorem"? Have you looked at Thevenin's theorem (and hence Thevenin equivalent circuits) yet?

3. Apr 14, 2013

Andrew187

This is my weakness this assignment is long overdue, I covered this last year now when I am going back through my notes it doesn't make sense:( But come to think of it yes you are correct I need to find the resistance of RL and then use that to find the maximum power transfer. I have covered thevenins and nortons but this task has to be calculated using kirchoffs to find the resistance of RL, I am lost.

4. Apr 14, 2013

Staff: Mentor

Use KVL and KCL to find the Thevenin equivalent. Then apply the Max Power theorem to find RL.

5. Apr 14, 2013

Andrew187

I still don't get it by thevanin equivalent and why I should use thevanin equivlent for this? I thought I had to use max power theorum once I determine the resistance for RL?

6. Apr 14, 2013

Staff: Mentor

That's exactly backwards Find the Thevenin equivalent first, than add the load RL and use the Max Power theorem to find the value of RL that maximizes the power in RL.

7. Apr 14, 2013

Andrew187

I don't get it can't I find the resistance of the load (RL) by using Kirchoffs? and then find the maximum power transfer using the maximum power theorum?

8. Apr 14, 2013

Staff: Mentor

Nope. Any value of RL will form a valid circuit that can be analyzed with KVL/KCL. There's no way to pick a particular value of RL from that.

The problem wants you to find the value of RL that maximizes the power transfer. To do that you need to apply the maximum power theorem. To apply the maximum power theorem you need to simplify the circuit to a form where it can be applied. The Thevenin equivalent is such a circuit.

So. First use Thevenin to reduce the network that will drive the load to its Thevenin equivalent. Then apply the max power theorem to the result to determine RL.

9. Apr 14, 2013

Andrew187

I'm lost now, it isn't making sense to me at all.

10. Apr 14, 2013

Staff: Mentor

Perhaps you should review the Max Power Transfer theorem. Take a look at the circuit used to prove it; The Max Power theorem allows you to find the load resistance RL that yields the maximum power transfer from a given source voltage with a series resistance.

This is the same form you should reduce your circuit to in order to apply the theorem to find your value of RL.

11. Apr 14, 2013

Andrew187

So from what point do I change what I have done in my work? or do I just start all over again?

12. Apr 14, 2013

Staff: Mentor

You'll have to decide how you want to go about finding the Thevenin equivalent for the network. You may be able to salvage some of the work you've done. For example, your value of I2 will let you find the open circuit voltage at the network terminals.

13. Apr 15, 2013

Andrew187

OK I am going to salvage the first part which for I2 I got 0.293a I belive the second bit is nonsense so how do I calculate the voltage output (Vo=V_EF) without load (Rl=∞)?

14. Apr 15, 2013

Staff: Mentor

What component is the Vo across?

15. Apr 15, 2013

Andrew187

Is it across all the resistors, R7,R8,R9,R10?

16. Apr 15, 2013

Staff: Mentor

Pick one... which resistor would you place the leads of a meter across in order to measure Vo?

17. Apr 15, 2013

Andrew187

Between R8 and R10 ?

18. Apr 15, 2013

Staff: Mentor

No. The load (RL) is not connected between R8 and R10. What component is RL in parallel with?

19. Apr 15, 2013

Andrew187

R10 so would I measure across E and F?

20. Apr 15, 2013

Staff: Mentor

Right.

Now, where does your I2 flow....

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21. Apr 15, 2013

Andrew187

I2 flows in R8 R9 and R10?

22. Apr 15, 2013

Staff: Mentor

Yes, so what's Vo?

23. Apr 15, 2013

Andrew187

R8+R9+R10/ 0.293a= 25Ω+7Ω+24Ω/ 0.293a= 5.23v is that correct?

24. Apr 15, 2013

Staff: Mentor

No. Vo is across R10 only! You know the current through R10. Vo is equal to the potential drop across R10. So use Ohm's law on R10.

25. Apr 15, 2013

Andrew187

V =IR= V= 0.293a*24Ω=7.032v