Practice Problems: Capacitors and Dielectrics
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1. (easy) A parallel plate capacitor is filled with an insulating material with a dielectric constant of 2.6. The distance between the plates of the capacitor is 0.0002 m. Find the plate area if the new capacitance (after the insertion of the dielectric) is 3.4 μF.
2. (easy) If a parallel plate capacitor (filled with an insulator) went through the following changes simultaneously, how would the capacitance be effected?
k doubles
plate separation halves
plate area quadruples
3. (moderate) A square parallel plate capacitor (length of each side = x) with plate separation d and a circular parallel plate capacitor (diameter = x and separation d) are both filled with the same dielectric material (k = 3.8). Which of the capacitors have a larger capacitance? Explain your answer. Given that the length of the square plates is 1.65 m, determine the k for the dielectric that must be inserted into the circular capacitor so that equal capacitance results for each capacitor.
4. (moderate) During a lightning storm the potential difference between a cloud and the ground can be extremely high. If this difference is 1.5x109 v (ground relative to cloud) and -19 C of charge (via movement of electrons) is transferred from the cloud to the ground during a lightning strike, determine the following:
a. How much work is done by the E-field?
b. If this work was performed on a truck with a mass of 10000 kg, find the speed that can be attained by the truck if started from rest.
5. (moderate) A capacitor is fully charged by a battery and then disconnected. An insulator is then inserted into the capacitor. Explain how each of the following would change.
a. The capacitance
b. The voltage
c. The E-field
d. The charge on the surface of the insulator
e. The charge on the plates
6 (moderate) Repeat the previous question, but assume that the battery stays connected to the capacitor during the insertion.
a. The capacitance
b. The voltage
c. The E-field
d. The charge on the surface of the insulator
e. The charge on the plates
7. (moderate) A capacitor (Co = 400 μF and A = 0.3 m2) is charged by a 50 volt battery. Determine the charge on the capacitor plates and the net E-field between the plates of the capacitor. Next, assume that the battery is disconnected after fully charging the capacitor. Find the charge and net E-field after a piece of plastic (K = 3.0) is inserted in between the plates. Finally, determine the E-field induced within the dielectric by the polarization of the dielectric.
8. (moderate) Repeat the previous problem assuming that the battery remains connected to the capacitor.
9. (easy) Watch the video below. The distance between the electrodes is 2.6 cm. If the dielectric strength of the dry air between the electrodes is 3x106 v/m, what is the voltage across the electrodes when the arc first forms?
Please supplement these problems with those found in your companion text.