physics
posted by Edwin .
A 24V battery of internal resistance of 10ohms is connected to a variable resistor. At what value of current drawn from battery the rate of heat produced by the resistor is maximum? Hence find its value.

Delivered power is a maximum when the internal and external resistances are equal, as I recall. Therefore
Rexternal(optimum) = 10 ohms.
Current with that external resistance
= V/Rtotal = 24/20 = 1.2 Amps
Maximum power produced in external resistor =
I^2*Rexternal = (1.2)^2 * 10 = 14.40 W
Check: If I use Rexternal = 11 ohms instead, Rtotal = 21 ohms and I = (24/21) = 1.143 A
I^2 * Rext = 14.37 W
If you use Rexternal = 9 ohms, your will still get a power less than 14.4 W