Most household power in North America is 120 V alternating current (VAC). Howeve

Question

Most household power in North America is 120 V alternating current (VAC). However, some high-power appliances such as electric ranges and clothes dryers typically require a special 220 V circuit. In this problem, you will calculate the energy, power, and current required by a dryer. You will also compare different methods of storing the energy required to run this appliance in a typical drying cycle.

Consider a dryer that operates on 220 V electricity, and it consumes an average power of 3200 W. For this homework, the “Alternating Current” part of the story is irrelevant, so please use our ordinary DC equations.

For each problem, show your algebra and your answer with units

1. Most of the power consumed by the dryer goes into producing heat. Dryers have a “heating element” which is a long coil of wire and can be treated as a single resistor. Using the value of power, and the operating voltage, calculate this resistance.

2. What is the average current drawn by the dryer?

3. A USB port can be used as a 5 V, 500 mA DC power supply. How many USB ports would it take to produce 3200 W?

4. Suppose the typical drying cycle takes 45 minutes, and you wanted to use the energy stored in a capacitor to power the dryer. If you use a capacitor that is charged up to a 220 V potential difference, and the separation between the plates is 0.2 mm what would the area of the plates need to be (in m2)? Does this size seem practical? (Calculate the size of each side, if it was a square plate. Set this in context, how big is this in terms of the world around us?)

5. A cubic meter of “natural gas” (mostly methane) at atmospheric pressure contains about 35 MJ of usable energy. How much natural gas (in m3) would it take to power the dryer for 45 minutes? Make an estimate (this means getting the order of magnitude right) of how much it would cost to purchase this much gas. Does the number seem reasonable?

6. Energy can also be stored by pumping water up to an elevated reservoir. The gravitational potential energy of the water can be converted to electricity by using a turbine generator as the water flows downhill. If the reservoir is 20 m high, and the turbine can convert 90% of the water’s potential energy to electricity, how many cubic meters of water must be stored to power the dryer for 45 minutes? (1 m3 of water = 1000 kg) Briefly, comment on the “real world” size of this result.

Explanation / Answer

Given:
Voltage,V= 220V & Power, P= 3200W
Now,
1) Let the resistance be R.
P= V^2 /R => R= V^2 /P = 15.125 Ohm.
2) Let the avg current be I.
So, I = V/R = 14.55 A
3) Power supplied by one USB port is:
P1= V*I = 5* 500*10^(-3) = 2.5 W
Hensed, no of USB ports required,n= 3200/2.5 = 1280
4) Energy is give by:-
E= P*time = 3200*45*60=
Also, we know that, Energy in a capacitor is given as:-
E(c)= 1/2 *C*V^2 => E= 1/2 *C*V^2
So, C = 2E/V^2 = 357.03 F
Now, C= (epsillon)* Area(A) / seperation(d)
=> A= 357.03* 0.2*10^(-3) /8.85*10^(-12)
So, A= 8.1*10^9 meter.
Such a big area is not possible practically.

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