Question

A 630-W space heater is designed for operation in Germany, where household electric outlets supply 230 V (rms) service. What is the power output of the heater when plugged into a 120-V (rms) outlet in a house in the United States? Ignore the effects of temperature on the heater's resistance.

Answer 1

Voltage in Germany = 230V

Power of heater = 630 watts = Current drawn by Heater in Germany (I) X Voltage applied (V)

630 Watts = I X 230 So I = 630 Watts/230V = 2.74Amps

Resistance of heater = 230V/2.74amps =83.9Ohms

If same heater is used in USA ,voltage applied= 120V

As a result of lesser Voltage(current driving energy) lesser current flows in USA in same heater.

Due to lesser current, Power dissipated as heat reduces ,since P= I^2R =V^2/R

Power drawn by heater in USA = V^2/R = 120V X 120V / 83.9ohms = 171.6 Watts

Note: The sentence suggesting to ignore rise of resistance due to Temperature is important,beacuse of slight increase in R due to increased temperature and consequent quicker movement of atoms,more effectively blocking curent.