26. Capacitors & Dielectrics

A parallel-plate capacitor is connected to a battery so that the left plate is connected to the positive terminal and the right plate is connected to the negative terminal. Which plate is the $\mathrm{positive}$ plate?

In an $RC$ circuit, what is the current through the resistor at the instant when the capacitor has acquired $\frac{1}{4}$ of its maximum charge?

Two 2.0 cm×2.0 cm metal electrodes are spaced 1.0 mm apart and connected by wires to the terminals of a 9.0 V battery. What are the charge on each electrode and the potential difference between them?

Capacitors can be used as “electric charge counters.” Consider an initially uncharged capacitor of capacitance C with its bottom plate grounded and its top plate connected to a source of electrons. If N electrons flow onto the capacitor’s top plate, show that the resulting potential difference V across the capacitor is directly proportional to N.

In a charged capacitor, where is the energy physically stored?

In the dynamic random access memory (DRAM) of a cell phone, each memory cell contains a capacitor for charge storage. Each of these cells represents a single binary-bit value of “1” when its 25-fF capacitor (1 fF = 10^-15 F )is charged at 0.6 V, or “0” when uncharged at 0 V. When fully charged, how many excess electrons are on a cell capacitor’s negative plate?

Paper has a dielectric constant K = 3.7 and a dielectric strength of 15 x 10⁶ V/m. Suppose that a typical sheet of paper has a thickness of 0.11 mm. You make a “homemade” capacitor by placing a sheet of 21 cm x 14 cm paper between two aluminum foil sheets (Fig. 24–40) of the same size. What is the capacitance C₀ of your device?

The capacitor shown in Fig. 24–34 is connected to an 80.0-V battery. Calculate (and sketch) the electric field everywhere between the capacitor plates. Find both the free charge on each capacitor plate and the induced charge on the faces of the glass dielectric plate.

Given a circuit where two capacitors, each with capacitance $C$, are connected in series, and this combination is connected in parallel with a third capacitor of capacitance $C$, what is the equivalent capacitance of the entire arrangement?

A capacitor is being charged in a simple RC circuit by connecting it to a battery at time $t=0$. Which graph best represents the charge $q$ on the positive plate of the capacitor as a function of time $t$?

Two capacitors are identical in size and shape, but one is filled with a dielectric material of dielectric constant $k$ while the other is empty ($\mathrm{vacuum}$ between the plates). If both are connected to the same voltage source, which statement is correct about their capacitances?

If three capacitors with capacitances $C_1$, $C_2$, and $C_3$ are connected in series, what is the expression for the total capacitance $C_{\text{total}}$ of the combination?

A $1.50\mu F$ capacitor is charging through a $16.0\Omega$ resistor using a $15.0V$ battery. What is the time constant $\tau$ of this RC circuit?

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?