Answer to Question #196459 in Electrical Engineering for JohnJeralNicolas

Question

A 48V battery has an internal resistance of 0.22 ohm and is connected to a variable resistance load through a line resistance of 1.28 ohms. For what value of load resistance will the load power be maximum and what will be the load current, load power and power loss under this condition

Answer 1

Maximum power in the external circuit, the battery will give when the load resistance is equal to the internal resistance of the current source. In our case $R=R_L+r=1.28+0.22=1.5\ (\Omega)$

The maximum value of useful power is reached in an external circuit at a current

$I_m=E/(2(R_L+r))=48/(2\cdot(1.28+0.22))=16\ (A)$

Maximum power at this current

$P_m=E^2/(4(R_L+r))=48^2/(4\cdot(1.28+0.22))=384\ (W)$

Power loss under this condition $P=384\ (W)$