26. Capacitors & Dielectrics

Four capacitors with capacitances $C_1$, $C_2$, $C_3$, and $C_4$ are connected in series. What is the equivalent capacitance of the combination?

Three capacitors, $C_1$ = $2 \mathrm{\mu F}$, $C_2$ = $4 \mathrm{\mu F}$, and $C_3$ = $6 \mathrm{\mu F}$, are connected such that $C_2$ and $C_3$ are in parallel, and this combination is in series with $C_1$. What is the net capacitance of the entire combination?

If three capacitors, each with capacitance $C$, are connected in series, what is the equivalent capacitance of the combination?

What is the primary role of the insulating material ($\mathrm{dielectric}$) placed between the plates of a $\mathrm{capacitor}$?

In an AC circuit with a capacitor, if the energy stored in the capacitor reaches the value calculated in part $\left(a\right)$ at its maximum, how many times per second does the capacitor reach this maximum energy value during one complete cycle of the alternating voltage?

When the switch in a circuit containing two capacitors in series is closed at $t=0s$, what happens to the total charge stored on the series combination immediately after closing the switch?

Suppose it takes 75 kW of power for your car to travel at a constant speed on the highway. If this capacitor were to be made from activated carbon (Section 24–2), the voltage would be limited to no more than 10 V. In this case, how many grams of activated carbon would be required?

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

For a parallel-plate capacitor with charge $Q$ stored on its plates and capacitance $C$, what is the voltage $V$ between the plates of the capacitor?

Why are the plates in a typical parallel-plate capacitor arranged parallel to each other?

Two capacitors, $C_1$ = $2\mu F$ and $C_2$ = $4\mu F$, are connected in series across a $12V$ battery. What is the charge stored on each capacitor?

Which physical property of an object is best quantified by its $\mathrm{capacitance}$?

A $2 mF$ capacitor is charged with $40 C$ of charge. What is the potential difference across the capacitor?

(I) Estimate the value of resistances needed to make a variable timer for intermittent windshield wipers: one wipe every 15 s, 8 s, 4 s, 2 s, 1 s. Assume the capacitor used is on the order of 1 μF. See Fig. 26–64.

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Three capacitors, $C_1$, $C_2$, and $C_3$, are each connected to the same battery of voltage $V$. Rank the capacitors in order of the charge stored on their positive plates, from greatest to least, if $C_1>C_2>C_3$.