26. Capacitors & Dielectrics

Which of the following is a primary function that a capacitor can perform in electrical circuits?

Six identical capacitors, each with capacitance $c$, are connected in three parallel branches, each branch containing two capacitors in series. What is the equivalent capacitance between the two ends of the network?

A circuit contains three capacitors: $C_1=2$ μF and $C_2=4$ μF are connected in series, and this combination is connected in parallel with $C_3=3$ μF. What is the net capacitance of the entire combination in μF?

Which of the following correctly gives the capacitance $C$ of a parallel plate capacitor with plate area $A$, plate separation $d$, and dielectric constant $\kappa$ (kappa)?

Two identical capacitors, one with capacitance $C$ and the other with capacitance $2C$, are each connected in separate circuits with identical resistors and initially charged to the same voltage. After the switch is closed in each circuit, which capacitor will discharge more quickly?

In a simple circuit with a battery, a switch, and a capacitor connected in series, after the switch is closed, which plate of the $C$ capacitor eventually becomes positively charged?

In an RC circuit, what is the expression for the time constant that characterizes the discharge of a capacitor through a resistor?

Two identical capacitors are connected in separate RC circuits, one with resistance $R=1\Omega$ and the other with $R=10\Omega$. Which capacitor discharges more quickly after being fully charged and then disconnected from the battery?

A circuit contains two capacitors, $C_1$ and $C_2$, connected in series across a battery of voltage $V$. If $C_1$=$4$$\mathrm{\mu F}$, $C_2$=$6$$\mathrm{\mu F}$, and $V$=$12$$V$, what is the charge on capacitor $C_1$?

Which property of a capacitor is directly affected by the frequency measured in $hertz$?

Which term describes the opposition to alternating current ($ac$) flow caused by a capacitor?

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

When two capacitors are connected in parallel, which of the following quantities must be the same for both capacitors?

Three capacitors with capacitances $C_1$ = $2 \mathrm{\mu F}$, $C_2$ = $4 \mathrm{\mu F}$, and $C_3$ = $6 \mathrm{\mu F}$ are connected in series. What is the total capacitance of the combination?

A cell membrane can be modeled as a parallel-plate capacitor. If the thickness of the membrane is $7.0 n^m$ and the area is $1.0 {\mathrm{\mu m}}^2$, what is the capacitance of the membrane? (Assume the dielectric constant $\kappa$ is $7.0$ and $\epsilon 0_{}$ = $8.85\times {10}^{-}$ F/m.)