circuit analysis - Maximum power transfer for unknown resistance

^{simulate this circuit – Schematic created using CircuitLab}

Hi,

I am trying to find out what should be the value of resistor connected across node 'ab' for maximum power transfer. So far I have tried working out by hand and I don't think I have got the right values. I have shorted out voltage source to find thevenin resistance and considered R1 parallel with (R2+R3) and (R4+R5). Can anyone please help me to find out equivalent thevenin circuit.

Answer

In order to find out Thevenize circuit, you want to do following things.

1. Temporary remove the load resistance(which is temoved here) whose current is required.


2. Find out the open circuit voltage Voc which appears across the 2 terminals from where resistance has been removed. It is called Thevenin voltage Ath.


3. Compute the Thevenin resistance, Rth of whole network as looked into from these 2 terminals(a and b) after all voltage sources have been removed leaving behind their internal resistances(if any) and current sources have been replaced by open circuit ie. infinite resistance.


4. Replace the entire network by a single Thevenin source, whose voltage is Vth or Voc and whose internal resistance is Rth or Ri.


5. Connect load resistance back to its terminals from where it was removed.


6. Finally calculate current flowing through load resistance Rl using equation, I= Vth/(Rth+Rl) or I= Voc/(Ri+Rl).

Maximum power transfer

According to maximum power transfer theorem, the maximum power Pmax=((V^2)/4Rl)=((V^2)/4Ri)

Or

We can simply say that when internal resistance of source,Ri= load resistance Rl, then the maximum power transfer happens...

According to me you want to put Thevenin's resistance, Rth across ab. Since the question is not providing information about internal resistance of V1, we can consider internal resistance zero while Thevenizing circuit (Some articles also saying we can make this consideration theoretically). But the system do not exists practically since there is no voltage source with zero internal resistance.

Sorry for typos. This answer may be false. Please critically think.