Efficiency and Work Done in Electric Systems: 5 Problems Solved

[lucianb]

Can anyone help me solving these problems:

1. A tension of 5V is measured between the ends of a wire. What was the work done by the electric field while a charge of 100C was passing through a cross-section of a wire? What is the resistance of the wire if the current flow lasted for 23 seconds?

2. The pressure reqired for the water system of a town consisting of four-storey buildings is that of a 24 m high water colunm. What is the daily consumption of electric energy used for the water system of a town with a popolation of 50000 if we count with a daily average of 100l per capita and if the efficiency of the pumps is 80% whereas that of the electric motors is 92%.

3. Concrete blocks, each having a mass of 2.4tons, must be transferred to a height of 16m and one block must be lifted every half minute.
The voltage of the elevator motor is 220V; its efficiency is 90%.
a) what is the power of the motor while lifting a block?
b) What is its current consumption during this time?
c) What is the electric energy used for the lifting of one block?
d) What does the electric elnergy used for lifting of one block cost?
(the price of 1kWh is 1.20Ft)

4. An aluminium wire and a copper wire, both of the same lenght, are connected in series to a battery. Equal amounts of heat are generated in them in equal times. what is the ratio between the cross sectional areas of the two wires?

5. We connect an incandescent lamp designed for a power of 24 W and a voltage of 12 V to a bettery having an internal resistance of 8 ohm. The voltage drop across the lamp has just the required value!
a) What is the electromotive force of the battery?
b) What is the efficiency of the circuit?

 

[Chen]

1. Let d be the length of the wire.

W_ele = F_eled
F_ele = qE

Can you find what E is? Remember that the electric field is constant throughout the wire and that V = Ed.

What is the definition of current?
I = dq/dt
So if a charge of 100c passes through the wire in 23 seconds, what is the current?

3. The work that has to be done on each block is equal to the change in its potential energy:
W_ext = ΔE_p = mgh
That work is provided by the electric motor. What is the expression for the work of the motor?
W_ele = Pt
Where P is the power of the motor and t is the time. So you have:
P = mgh/t
Where t is 30 seconds, as the question requires.

(b) P is defined as VI so you can find I. (c) The electric energy is the same as the work required to lift one block, which is Pt as I showed. (d) If 1kW per hour costs 1.20Ft, how much does 1kW per second cost? How much does 1kW per 30 seconds cost? How much kW's are required to lift the block?

4. If "Equal amounts of heat are generated in them in equal times" then the power of each wire is the same:
P₁ = P₂
R₁I₁² = R₂I₂²
You know they are connected in series, so the current through both wires is the same. Therefore:
R₁ = R₂
Now use the expression for resistance and see how it depends on the length, cross sectional area and the material.

5. What is the resistance of the lamp? Hint:
P = V²/R
Therefore what is the total resistance of the circuit? What must be the EMF of the battery so that the potential drop across the lamp is 12V?

 

[lucianb]

other problems

thanks for the help with the other problems. What about the ones you've missed?

I have 3 new ones. These are the last i will post !

1. We want to operate a 12V/15W lamp at its normal power, but we only have a battery of an electromotive force of 24V and an internal resistance of 3 ohm.
What should be the resistance of the resistor connected
a)in parallel
b)in series
with the lamp to ensure the desired operation
What is the efficiency of operation in each case?

2. When a pocket battery is short-circuited by a very thick copper wire, the battery gets considerably warmer whereas the copper wire remains cool. Why?

3. Which is the more economic way for transporting electric energy: the one using high voltage or the one using low voltage? Give a detailed explanation.

Thanks

 

[Chen]

I don't know 3.

1. Again, what is the resistance of the lamp and what's the current we want to have through it? Build the two circuits, once connect a resistor in parallel to the lamp and then in series. Build the expression for the total resistance of the circuit and the expression for the current through the lamp and find what kind of resistor will give you the desired result.

2. What's so special about a "very think" copper wire? How does it different from a thin copper wire? Can this influence the amount of heat that is developed in the wire when it is connected to a circuit?

 

[lucianb]

oops it's a very thin copper wire. forget 3, what about the other 3 that i posted! i really need help with these problems!

Lucian

 

[Chen]

No idea about 2 either. Sorry.

 

[lucianb]

ok, well thanks for the ones that u helped me with!

Lucian