Question

A 120 v potential difference is applied to a space heater whose resistance is 17 Ï when hot. (a) at what rate is electrical energy transferred to thermal energy? (b) what is the cost for 7.1 h at us$0.05/kw·h?

Answer 1

a) The rate at which electrical energy is transferred to thermal energy is equal to the power dissipated on the resistor because of the Joule effect:
$P= \frac{V^2}{R}= \frac{(120 V)^2}{17 \Omega}=847 W$

b) We can find the total energy dissipated in 7 h:
$E=Pt = (847 W)(7 h)=5929 Wh=5.93 kWh$
The energy costs 0.05 $ per kWh, so the total cost of 5.93 kWh of energy is
$5.93 kW \cdot 0.05 \frac{1}{kWh} =0.30$ $