The Iceberg Kid, infamous for imposing a deep freeze on whoever disagrees with h

Question

The Iceberg Kid, infamous for imposing a deep freeze on whoever disagrees with him, discovers that in his advanced teenaged years his hands constantly feel chilled. As he is a cool physics student, the lceberg Kid quickly calculates the resistance of the resistor needed to warm his hands. Given that 185 J of thermal energy is generated by the resistor during 9.81 s of operation while connected to a 12.0-V battery, find the correct value of this resistance (and avoid a cold, cold fate). Number Ohm

Explanation / Answer

Average power dissipated in the resistor P = W/t = i^2R, where W is the energy dissipated in the resistor

W = i^2Rt = (V/R)^2Rt = V^2t/R

185 = 12^2 x 9.81 / R

R = 12^2 x 9.81 / 185 = 7.64 ohm

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