Question

A clothes dryer in a home has a power of 4,500 watts and runs on a special 220-volt household circuit,

1.what is the resistance of the dryer?
2.what is the current through the dryer?
3.how many kilowatt-hours of electricity are used by the dryer if it used for 4 hours in one week?

Answer 1

The resistance of the 4,500-watt clothes dryer operating at 220 volts is 10.76 ohms, the current through it is 20.45 amperes, and if it's used 4 hours in a week, it consumes 18 kilowatt-hours of electricity.

Step-by-step explanation:

The electric clothes dryer question involves calculating the dryer's resistance, current through it, and energy used over a period. First, let's find the resistance of the dryer using Ohm's law (V = IR), which we can rearrange to R = V2/P. With a power (P) of 4,500 watts and a voltage (V) of 220 volts, the resistance is:

R = 2202/4500 = 10.76 ohms.

Next, we calculate the current through the dryer with the formula P = VI, solving for I gives us I = P/V:

I = 4500/220 = 20.45 amperes.

Lastly, we determine the energy usage in kilowatt-hours. The dryer uses 4,500 watts, which is 4.5 kilowatts, for 4 hours. Therefore, the total energy used is:

Energy = Power × Time = 4.5 kW × 4 hrs = 18 kWh.

Answer 2

1). Power = (voltage)² / (Resistance)

4,500 = (220)² / Resistance

Multiply each side by (resistance) : 4,500 x resistance = (220)²

Divide each side by 4,500 : Resistance = (220)² / 4,500 = 10.76 ohms


2). Power = (voltage) x (Current)

Divide each side by (voltage): Power / voltage = Current

4,500 / 220 = 20.45 Amperes


3). 4,500 watts = 4.5 kilowatts

(4.5 kilowatts) x (4 hours) = 18 kilowatt-hours