please help on maximum power transfer question

Thread Starter

RevitRed

Joined Dec 4, 2014
6
A Thevenin voltage generator consists of an ideal voltage source V(t) (given) in electrical series with an RL series combination (given R,L).a variable resistor is connected across this generator. if we adjust the the RL so that it dissipates maximum power what is the power dissipated by RL.

the voltage will be in the form Vmaxsin(wt).

can someone please check my work to see if it all checks out its really important i do well on this.




so i know that for maximum power transfer the Zth has to be equal to the Zload

here i know that Zth will be sqrt(R^2 +(w^2)(L^2) which is equal to Zload

so then Zload must be equal to Rload

the current going through the circuit will be

I = (Vmax/Zth + Zload)

and P = (Irms^2)(Rload) = (Rload/2)(Vmax/(Zth+Zload))^2

if this is not correct please any hints towards the answer would be appreciated
 

Thread Starter

RevitRed

Joined Dec 4, 2014
6
yes but in this case the load impedance is purely real it has no imaginary component, so would it not be that the Zload = Rload = sqrt(R^2 + (wL)^2)
 

WBahn

Joined Mar 31, 2012
26,398
A Thevenin voltage generator consists of an ideal voltage source V(t) (given) in electrical series with an RL series combination (given R,L).a variable resistor is connected across this generator. if we adjust the the RL so that it dissipates maximum power what is the power dissipated by RL.

the voltage will be in the form Vmaxsin(wt).

can someone please check my work to see if it all checks out its really important i do well on this.




so i know that for maximum power transfer the Zth has to be equal to the Zload

here i know that Zth will be sqrt(R^2 +(w^2)(L^2) which is equal to Zload

so then Zload must be equal to Rload

the current going through the circuit will be

I = (Vmax/Zth + Zload)

and P = (Irms^2)(Rload) = (Rload/2)(Vmax/(Zth+Zload))^2

if this is not correct please any hints towards the answer would be appreciated
I = (Vmax/Zth + Zload)

This is clearly not correct because the units don't work out. The first term, Vmax/Zth, is a current. You then add that to an impedance. Always check your units. And, yes, I know what you meant, but you need to learn to write what you mean.

You need to start with the power for an arbitrary load and then maximize it under the constraint that the load is purely real. This is actually easier than the unconstrained case because you only have one variable to work with, so just take the derivative with respect to that variable and set it equal to zero.
 
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