A certain electric furnace consumes 24 kw when it is connected to a 240-v line. what is the resistance of the furnace?

One very handy electrical formula is

Power dissipated by a resistance = (Voltage) ² / (resistance).

24 kilowatts = (240 v) ² / Resistance

Multiply each side by (Resistance):

(Resistance) x (24 kilowatts) = (240 v) ²

Divide each side by (24 kilowatts):

Resistance = (240 v) ² / (24,000 watts)

Resistance = (57,600 / 24,000) (volt² / volt · Amp)

Resistance = 2.4 (volt/Amp)

Resistance = 2.4 Ohms