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# Parallel-plate capacitors

(See attached file for full problem description)
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1. A parallel-plate air capacitor has a capacitance of 920 pF. The charge on each plate is 2.55µC
a. What is the potential difference between the plates?
b. If the charge is kept constant, what will be the potential difference between the plates if the separation is doubles?
c. How much work is required to double the separation?

2. A parallel-plate capacitor has the space between the plates filled with two slabs of dielectric, one with constant k1 and one with constant k2. Each slab has thickness d/2, where d, is the plate separation. Show that the capacitance is

C = (2E0A/d)( k1 k2/ k1+ k2)

3. The current in a wire varies with the time according to the relation
I = 55 A - (0.65 A/s2)t2

a) How many coulombs of charge pass a cross section of the wire in the interval between t = 0 and t = 8.0s?
b) What constant current would transport the same charge in the same time interval?

4. A complete circuit consists of a 24.0 V battery, a 5.60 omega resistor, and a switch. The internal resistance of the battery is 0.28 omega. The switch is opened. What does an ideal voltmeter read when placed,
a) across the terminal of the battery
b) across the resistor
c) across the switch
d) repeat part a b and c when the switch is closed.

5. A resistor with a 15.0 V potential difference across its ends develops thermal energy at a rate of 327 W.
a) What is its resistance?
b) What is the current in the resistor?

6) Prove that when two resistors are connected in parallel, the equivalent resistance of the combination is always smaller than that of either resistor.

7) Each of the resistors below has a resistance of 2.4 omega and can dissipate a maximum of 36W without becoming excessively heated. What is the maximum power the current can dissipater?
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