Determine the value of the load resistance RL in the figure that gives maximum power dissipation

Explanation:

Electric power is given by the formula

P = VI

as current is given by

I = V/R

P = V²/R is also a valid formula

This means that for a constant voltage V, the maximum power will occur when the Resistance is at a minimum.

for the circuit, the equivalent resistance is

Re = 2 + 1/(1/8 + 1/R₁)

For minimum Re, we need the right hand term to be as small as possible.

For the right hand term to be small, we want the denominator (1/8 + 1/R₁) to be very large. This will approach the largest value when R₁ approaches zero Ω to make 1/R₁ approach infinity.

R₁ = 0 makes Re = 2 Ω

P = 24²/2 = 288 W(atts) which will be the maximum possible power dissipation provided that the 2Ω resistor is capable of handling the heat. It will be carrying 100% of the current. The 8Ω resister will carry 0% of the current.

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