26. Capacitors & Dielectrics

Three capacitors with capacitances $C_1$, $C_2$, and $C_3$ are connected in series. What is the equivalent capacitance $C_{\mathrm{eq}}$ of the combination?

Two capacitors with capacitances $C_1$ and $C_2$ where $C_1>C_2$ are connected in parallel to a battery of voltage $V$. Which statement is correct about the charge stored on each capacitor?

A system consists of four capacitors connected as shown, with a potential difference of $50.0V$ applied across points a and b. If the capacitances are $C_1$ = $2.0\mathrm{\mu F}$, $C_2$ = $4.0\mathrm{\mu F}$, $C_3$ = $6.0\mathrm{\mu F}$, and $C_4$ = $12.0\mathrm{\mu F}$, what is the equivalent capacitance between a and b if $C_2$ and $C_3$ are in series and their combination is in parallel with $C_4$, and this whole group is in series with $C_1$?

Which of the following devices can store large amounts of electrical energy for later use?

When two or more capacitors are connected in series across a potential difference, which of the following statements is correct?

(II) Use Gauss’s law to show that $\overrightarrow{E}=0$ inside the inner conductor of a cylindrical capacitor (see Fig. 24–7 and Example 24–2) as well as outside the outer cylinder.

The long cylindrical capacitor shown in Fig. 24–37 consists of four concentric cylinders, with respective radii R_a, R_b, R_c and R_d. The cylinders b and c are joined by metal strips. Determine the capacitance per unit length of this arrangement. (Assume equal and opposite charges are placed on the innermost and outermost cylinders.)

A parallel-plate air capacitor has a capacitance of $920pF$ and the charge on each plate is $3.90\mathrm{bc}C$. What is the potential difference between the plates?

(II) Two different dielectrics fill the space between the plates of a parallel-plate capacitor as shown in Fig. 24–31. Determine a formula for the capacitance in terms of K₁, K₂, the area A of the plates, and the separation d₁ = d₂ = d/2. [Hint: Can you consider this capacitor as two capacitors in series or in parallel?]

A parallel-plate capacitor with capacitance $C$ is connected to a battery that provides a constant voltage $V$. What is the charge $Q$ stored on the capacitor?

Consider an air-filled charged capacitor. Which of the following actions will increase its capacitance?$$

Three capacitors with capacitances $C$, $2C$, and $3C$ are connected in series. What is the equivalent capacitance of the combination?

(I) The two plates of a capacitor hold +3500 μC and -3500μC of charge, respectively, when the potential difference is 960 V. What is the capacitance?

A parallel-plate capacitor with plate area 2.0 cm² and air-gap separation 0.50 mm is connected to a 12-V battery, and fully charged. The battery is then disconnected. What is the charge on the capacitor?