Q: For the circuit in the previous question, what is the charge on the $$6.00\ \mu\mathrm{F}$$ capacitor?

$$Q = 6.75\ \mathrm{V} \times 6.00\ \mu\mathrm{F} = 40.5\ \mu\mathrm{C}$$

Question 1

What is the equivalent capacitance of the three capacitors in the first figure (20 μF and 30 μF in parallel, then in series with 25 μF)?

Accepted Answer

$$C_{eq} = \left[ (20 + 30$$)^{-1}$$ + 25$$^{-1}$$ \right]^{-1} = 14.7\ \mu\mathrm{F}$$

Question 2

Two capacitors of capacitance $$6.00\ \mu\mathrm{F}$$ and $$8.00\ \mu\mathrm{F}$$ are connected in parallel. The combination is then connected in series with a $$14.0\ \mu\mathrm{F}$$ capacitor and a $$12.0\ \mathrm{V}$$ battery. What is the equivalent capacitance of this combination?

Accepted Answer

$$C_{eq} = \left[ (6.00 + 8.00$$)^{-1}$$ + 14.0$$^{-1}$$ \right]^{-1} = 7.88\ \mu\mathrm{F}$$

Question 3

For the circuit in the previous question, what is the charge on the $$6.00\ \mu\mathrm{F}$$ capacitor?

Accepted Answer

$$Q = 6.75\ \mathrm{V} 	imes 6.00\ \mu\mathrm{F} = 40.5\ \mu\mathrm{C}$$

Question 4

A $$15\ \mu\mathrm{F}$$ air-filled capacitor is connected to a $$50\ \mathrm{V}$$ voltage source and becomes fully charged. The voltage source is then removed and a slab of dielectric with $$k = 5.0 is $$inserted. What is the new capacitance?

Accepted Answer

$$C' = 75\ \mu\mathrm{F}$$

Question 5

After inserting the dielectric in the previous question, what is the potential difference across the plates?

Accepted Answer

$$V' = 10\ \mathrm{V}$$

Question 6

A dielectric with dielectric constant $$k = 4 is $$inserted into a parallel plate capacitor, filling $$1/3 of $$the volume. The capacitance without dielectric is $$C. $$What is the new capacitance?

Accepted Answer

$$C' = C \left( \frac{2 + k}{3} \right) = C \left( \frac{2 + 4}{3} \right) = 2C$$

Question 7

An ideal parallel‐plate capacitor stores energy $$U_0$$ when the plate separation is $$d. If $$the separation is doubled (battery disconnected), what is the new stored energy?

Accepted Answer

$$U = \frac{U_0$}{2}$$

Question 8

An air-filled capacitor stores $$6.00\ \mathrm{mJ} of $$energy. It is then filled with water ($$k = 78) $$without discharging. What is the new stored energy?

Accepted Answer

$$U' = \frac{6.00\ \mathrm{mJ}}{78} = 0.077\ \mathrm{mJ}$$

Question 9

In the circuit with four identical capacitors and a switch (see figure), after the switch is thrown to position B, what is the ratio of the charges on the capacitors?

Accepted Answer

$$Q_1$$ : $$Q_2$$ : $$Q_3$$ : $$Q_4 = 2$$:1:1:1$$

Question 10

The capacitors in the network shown (all $$5.0\ \mu\mathrm{F}) $$are connected as in the figure. What is the equivalent capacitance $$C_{ab}$$?

Accepted Answer

$$C_{ab} = 7.5\ \mu\mathrm{F}$$

Question 11

Three capacitors are arranged as shown: $$C_1 = 5.0$$\ \mathrm{pF}$$, C_2$ = 10.0\ \mathrm{pF}$$, $$C_3 = 15.0$$\ \mathrm{pF}$$. If the voltage across C_2$ is 311$$\ \mathrm{V}$$, what is the total voltage across the arrangement?

Accepted Answer

$$V_{total} = 466.5\ \mathrm{V}$$

Question 12

A $$40.0\ \mu\mathrm{F}$$ capacitor is initially charged to $$5.00\ \mu\mathrm{C}$$, and then connected in a circuit with three uncharged capacitors ($$10.0\ \mu\mathrm{F}$$, $$14.0\ \mu\mathrm{F}$$, $$15.0\ \mu\mathrm{F}) as $$shown. What is the final total energy stored in the system after the switch is closed for a long time?

Accepted Answer

$$U_{final} = 0.313\ \mu\mathrm{J}$$

Question 13

A network of capacitors is connected to a $$100\ \mathrm{V}$$ battery as shown. What is the total energy stored in the seven capacitors?

Accepted Answer

$$U = 0.18\ \mathrm{J}$$

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