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Integrated ConceptsHydroelectric generators (see Figure 20.46$)$ at Hoover Dam produce a maximum current of $8.00 \times 10^{3}$ A at 250 $\mathrm{kV}$ . (a) What is the power output? (b) The water that powers thegenerators enters and leaves the system at low speed (thus its kinetic energy does not change) but loses 160 m in altitude. How many cubic meters per second are needed, assuming 85.0% efficiency?

(a) $P=2.00 \times 10^{9} \mathrm{W}$(b) $V / \Delta t=1.50 \times 10^{3} \mathrm{m}^{3} / \mathrm{s}$

Physics 102 Electricity and Magnetism

Chapter 20

Electric Current, Resistance, and Ohm's Law

Current, Resistance, and Electromotive Force

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09:29

In physics, a current is a…

11:26

03:55

Hydroelectric generators (…

01:43

Water falls over a dam of …

03:37

In a hydroelectric dam, wa…

06:39

A hydroelectric dam holds …

11:01

03:06

A generator at a dam can s…

02:41

Hoover Dam on the Colorado…

03:19

02:17

The Grand Coulee Dam is 12…

04:05

Suppose a power plant deli…

10:13

03:01

Water flows $(v \approx 0)…

02:00

Some electric-power compan…

05:54

A hydroelectric power faci…

01:52

A river flowing steadily…

06:45

04:32

Each second, 1200 $\mathrm…

04:50

A power plant, having a Ca…

06:14

03:40

Water flows over a dam at …

Ask for the given information who dam produces a current, which is of 8 into 10, raised to 3 amperes so write as i is equal to 8 into 10 to 3, so it is around 8000 amperes and the voltage is given us 250 kilo volts now to Calculate the power output will start with the staple a in order to calculate power which is given as i multiplied by v. Value of current is given as 1810 to 3 amperes multiplied by 250, kilovolts 10 to 3 vols. After calculating this, we get the value as 2 into 10, raised to 9 wattstherefore. Il write. P is equal to 10, raise 2 into 10, raise to 9 watts. Next will move to step bow. This particular energy is equivalent to the potential energy of the water with almost 85 percent efficiency, so p is equal to 85 percent to that of potential energy of water, so 85 percent of since potential energy is mass multiplied by gravitation force, multiplied by height. So in this case, we can calculate the mass of water. So therefore i'll write it as p is equal to 85 divided by 100, that is 0.85 multiplied by mass anti gravitation force into height, so we'll get it in terms of mass, which is b divided by 0.85 into g into h. Therefore, let's put the values. P s 2 into 10 to 9, what's 0.85 multiplied by 9.8 meter per second square multiplied by height, as given us 160 meter. So when we calculate mass, therefore mass is equal to 1.501 into 10 to 6 kilograms. This is the second answer that we get it here: let's move to the next 1, that is steps to calculate how many cubic meters per second are needed. So, in order to calculate this particular volume, we use the formula as mass divided by density of water, which is denoted an let's put the values as masses 1.501 into 10, raise to 6 kilograms, divided by 1000 kilograms per meter cube, which is the density of water. Ultimately, we get answered as 151 meter cube, which we can write as 1.5 in tents, 23 meter cube per second. So therefore answer the question asked 1.5 into 10, raise to 3 cubic meters per second water needed with 85 percent of efficiency. This is the answer that we get right:

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