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Chapter 24
1. Two conductors insulated from each other are charged by transferring electrons from one
conductor to the other. After 1.6 X 1012 electrons have been transferred, the potential difference
between the conductors is found to be 14 V. What is the capacitance of the system?
2. An isolated charged conducting sphere of radius 12 cm creates an electric field of 4.9 X 104
N/C at a distance of 21 cm from its center.
a) What is its surface charge density?
b) What is its capacitance?
3. When a potential difference of 150 V is applied to the plates of a parallel-plate capacitor, the
plates carry a surface charge density of 30 nC/cm2. What is the spacing between the plates?
4. A 50-m length of coaxial cable has an inner conductor with a diameter of 2.58 mm and a
charge of +8.1 μC. The surrounding conductor has an inner diameter of 7.27 mm and a charge of
-8.1 μC.
a) What is the capacitance of this cable?
b) What is the potential difference between the two conductors?
5. A cylindrical capacitor has outer and inner conductors whose radii are in the ratio b/a = 4/1.
The inner conductor is to be replaced by a wire whose radius is one half of the original inner
conductor. By what factor should the length be increased in order to obtain a capacitance equal
to that of the original capacitor?
6. An air filled spherical capacitor is constructed with inner and outer shell radii of 7 and 14 cm,
respectively.
a) Calculate the capacitance of the device.
b) What potential difference between the spheres will results in a charge of 4 µC on each
conductor?
7. How many 0.25-pF capacitors must be connected in parallel in order to store 1.2 µC of charge
when connected to a battery providing a potential difference of 10 V?
8. A group of identical capacitors is connected first in series and then in parallel. The combined
capacitance in parallel is 100 times larger than for the series connection. How many capacitors
are in the group?
9. Two capacitors C1 = 25 µF and C2 = 5 µF, are connected in parallel and charged with a 100-V
power supply.
a) Calculate the total energy stored in the two capacitors.
b) What potential difference would be required across the same two capacitors connected in
series in order that the combination store the same energy as in (a)?
10. A 16-pF parallel-plate capacitor is charged by a 10-V battery. If each plate of the capacitor
has an area of 5 cm2, what is the energy stored in the capacitor? What is the energy density
(energy per unit volume) in the electric field of the capacitor if the plates are separated by air?
11. When the voltage applied to a capacitor increases from 80 V to 110 V, the charge on the
capacitor increases by 9.0 X 10-5 C. Determine the capacitance.
12. An isolated capacitor of unknown capacitance has been charged to a potential difference of
100 V. When the charged capacitor is then connected in parallel to an uncharged 10-µ F
capacitor, the voltage across the combination is 30 V. Calculate the unknown capacitance.
13. A parallel-plate capacitor is constructed using a dielectric material whose dielectric constant
is 3 and whose dielectric strength is 2 X 108 V/m. The desired capacitance is 0.25 µF, and the
capacitor must withstand a maximum potential difference of 4000 V. Find the minimum area of
the capacitor plates.
14. A parallel-plate capacitor is constructed using three different dielectric materials, as shown.
a) Find an expression for the capacitance of the device in terms of the plate area A and d, k1, k2,
and k3.
b) Calculate the capacitance using the values A = 1 cm2, d = 2 mm, k1 = 4.9, k2 = 5.6, and
k3 = 2.1.