One formula for the power dissipated by a resistor is
Power = (current)² · (resistance)
I have a feeling that this would be a handy formula to use to solve this problem.
66 W = (current)² · (148 Ω)
Current = √(66/148)
Current = 0.668 Ampere
The total power being delivered by the battery is . . .
Power = (voltage) · (current)
Power = (523 volts) · (0.668 Amp)
Total battery power = 349.4 Watts
66 Watts is being dissipated by the heating element. The rest of the humongous power delivered by the battery is being dissipated by the battery's own internal resistance.
Power = (349.4 - 66)
Power = 283.4 watts
As a working electrical engineer, I'm required to pound on the desk and protest this expensive and unhealthy situation.
-- The battery is enormous ... 523 V ! ... and must weigh a ton.
-- The battery itself is using 81% of the power it's being used to deliver.
-- And all this is just to operate a measly 66W heater !
-- You can probably get just as much heat out of the heater in the truck you'll need to shlep this battery around to where the heat is needed.
