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Electricity
"Proof" Exercises Question 1
A battery has an emf,
 , and internal resistance, r. The battery is connected to a variable resistor, R, as shown below. |
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| a) |
As the variable resistor is varied, the power dissipated in it will also vary. Show that the power, P, dissipated in the variable resistor is given by |
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| b) |
If
= 9V and r = 3W, what is the maximum value of the power dissipated in the variable resistor, R? |
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You might know a mathematical method for finding the maximum value of a function. If not, you will have to make a guess as to what value of R will result in the maximum power being supplied to it.
If R >> r then the power dissipated in the variable resistor is very low (try, say, R = 300 W ...); similarly, if R << r, P is very low (try, for example, R = 0·03W ...). So, how about R = ??... |
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Question 2
| An electron of charge, e, and mass, m, enters the uniform electric field between two parallel charged plates, as shown in the diagram below. |
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| The p.d. across the plates is V and the distance between them is d. The initial velocity of the electron is of magnitude, u and is parallel to the plates. The point of entry into the field is midway between the two plates. The electron hits the lower plate after having moved a distance x in the field (x measured parallel to the plates). Show that |
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© David Hoult 2008 |
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