4. A 120 V potential difference is applied to a space heater whose resistance is 14 Ω when hot. a) At what rate is electrical energy transferred to thermal energy? b) What is the cost for 5.0 h at $0.05/kWh?

a) P = 1028.6 W = 1.03 KW

b) Cost = $0.25

Explanation:

a)

The rate of electrical energy transfer or power of the heater is given as:

P = VI

where,

P = Rate of Electrical Energy Transferred = ?

V = Potential Difference = 120 V

I = Current

but, from Ohm's Law:

V = IR

I = V/R

Therefore,

P = V²/R

where,

R = Resistance = 14 Ω

Therefore,

P = 120²/14

P = 1028.6 W = 1.03 KW

b)

First we find energy used:

Energy = E = Pt

where,

t = time = 5 h

Therefore,

E = (1.03 KW)(5 h)

E = 5.14 KWh

Now, the cost is given as:

Cost = (E)(Unit Price)

Cost = (5.14 KWh)($0.05/KWh)

Cost = $0.25