Physics 1220 In-Class Problems: Capacitors

1. In the figure below, C₁ = C₅ = 3.00 μF and C₂ = C₃ = C₄ = 2.00 μF. What is the equivalent capacitance of the circuit? A potential of 600 V is applied across points A and B.  What is the charge on each capacitor? What is the voltage across each capacitor? What is the energy stored in each capacitor? Put your results in a table.

   

2. What is the equivalent capacitance of the circuit shown below? A potential of 24 V is applied across points A and B.  What is the charge on each capacitor? What is the voltage across each capacitor? What is the energy stored in each capacitor? Put your results in a table.

   

Charged Capacitor Circuits

3. A 4.00 μF capacitor and an 8.00 μF capacitor are separately charged by a 20.0 Volt power supply. The capacitors are then placed in the circuit shown below.
   (a) What is the charge on each capacitor when the switch is open?
   (b) What will be the charge and polarity on each capacitor when the switch is closed?

   
   

4. A 4.00 μF capacitor and an 8.00 μF capacitor are separately charged by a 20.0 Volt power supply. The capacitors are then placed in the circuit shown below. What will be the charge on each capacitor when the switch is closed? (Note that the polarities are switched from the previous question.)
   
5. A 10 mF capacitor is charged to 10 V while a 20 mF capacitor is charged to 5 V. They are then placed in the circuit below with given orientation. What will be the charge and voltage drop across each capacitor when the switch is closed?



6. A 10 mF capacitor is charged to 10 V while a 20 mF capacitor is charged to 5 V. They are then placed in the circuit below with given orientation. What will be the charge and voltage drop across each capacitor when the switch is closed? (Note that the polarities are switched from the previous question.)




Dielectrics

7. Two oppositely charged conducting plates, with equal magnitude of charge per unit area, are separated by a dielectric 3.00 mm thick, with a dielectric constant of 4.50. The resultant electric field in the dielectric is 1.60 × 10⁶ V/m. Compute (a) the charge per unit area on the conducting plates, and (b) the charge per unit area on the surfaces of the dielectric.
8. Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electric field is 3.60 × 10⁶ V/m. When the space is filled with a dielectric, the electric field is 1.20 × 10⁵ V/m. (a) What is the charge density on the surface of the dielectric? (b) What is the dielectric constant?
9. A capacitor that has air between its plates is connected across a potential difference of 12 V and stores 48 μC of charge. It is then disconnected from the source while still charged. (a) Find the capacitance of the capacitor. (b) A piece of Teflon (κ = 2.1) is inserted between the plates. Find the voltage and charge on the capacitor. (c) Find its new capacitance.
10. Determine (a) the capacitance and (b) the maximum voltage that can be applied to a Teflon-filled parallel-plate capacitor having a plate area of 1.75 cm² and dielectric thickness of 0.04 mm. Breakdown occurs when the electric field exceeds 60 × 10⁶ V/m.
11. Three 10-μF capacitors are connected in parallel. A dielectric κ = 2.0 is inserted into one of the capacitors. The capacitors are then connected to a 4.0 V battery. (a) What is the charge on each capacitor and what is the energy stored by each capacitor? (b) The battery is disconnected. The dielectric is then removed from the capacitor. What is the new charge on each capacitor and what now is the energy stored by each capacitor? (c) What happened to the lost energy?

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Questions? mike.coombes@kwantlen.ca