Question

A 3.00 kW space heater designed for use in a European country where the rms voltage is 225V is being used in a US household wher ethe rms voltage is 110.0 V. Ignoring the effect of temperature on the heater's resistance, determine the power output of the heater in the American household. Find also the peak currents through the heater in the two households.

Answer 1

P = power of heater in european country = 3000 W

V_rms = ms voltage in european country = 225 V

R = resistance of heater

Using the formula ::

R = V²_rms /P

R = (225)² /3000

R = 16.875 ohm

in america ::

V'_rms = 110 V

hence power output is given as

P' = V'²_rms /R

P' = 110² / (16.875)

P' = 717.04 Watt

in european country ::

rms current through heater is given as ::

I_rms = V_rms /R = 225 /16.875 = 13.33 A

peak current = 1.41 I_rms = 1.41 x 13.33 = 18.8 A

in american country ::

rms current through heater is given as ::

I_rms = V_rms /R = 110/16.875 = 6.52 A

peak current = 1.41 I_rms = 1.41 x 6.52 = 9.2 A