Question 24.6: A 220 V potential difference is maintained across an electri......

Principles of Physics for Scientists and Engineers [1418166]

A 220 V potential difference is maintained across an electric heater that is made from a nichrome wire of resistance 20 Ω. (a) Find the current in the wire and the power rating of the heater. (b) At an estimated price of 0.35 LE (Egyptian pound) per kilowatt-hour of electricity, what is the cost of operating the heater for 2h?

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(a) Using ΔV = I R, we get:

I={\frac{\Delta V}{R}}={\frac{220\,\mathrm{V}}{20\,\Omega}}=11\,\mathrm{A}

Using the power expression P = I² R, we find that:
P = I² R = (11 A)²(20 Ω) = 2,420 W
(b) The amount of energy transferred in time Δt is P Δt. Thus:
P Δt = (2,420 W)(2 h) = 4,840 Wh = 4.84 kWh
If energy is purchased at 35 piaster per kilowatt-hour then the cost is:
Cost = (4.84 kWh)(0.35 LE/kWh) = 1.69 LE

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