Question 26.45: A 1250 W radiant heater is constructed to operate at 115 V. ......

THINK Let P be the power dissipated, i be the current in the heater, and V be the potential difference across the heater. The three quantities are related by P = iV.

EXPRESS The current is given by i = P/V. Using Ohm’s law V = iR, the resistance of the heater can be written as

R=\frac{V}{i}=\frac{V}{P / V}=\frac{V^2}{P} .

ANALYZE (a) Substituting the values given, we have i=\frac{P}{V}=\frac{1250 \,W }{115\, V }=10.9 \,A .

(b) Similarly, the resistance is

R=\frac{V^2}{P}=\frac{(115\, V )^2}{1250 \,W }=10.6\, \Omega .

(c) The thermal energy E generated by the heater in time t = 1.0 h = 3600 s is

E=P t=(1250 \,W )(3600 \,s )=4.50 \times 10^6\, J .

LEARN Current in the heater produces a transfer of mechanical energy to thermal energy, with a rate of the transfer equal to  P = iV =V² / R.