26. Capacitors & Dielectrics

Two capacitors, $C_1$ and $C_2$, are connected in series across a battery of voltage $V$. What is the voltage $V_1$ across the first capacitor $C_1$?

(II) Consider the circuit shown in Fig. 26–67, where all resistors have the same resistance R. At t = 0, with the capacitor C uncharged, the switch is closed. At t = ∞, the currents can be determined by analyzing a simpler, equivalent circuit. Identify this simpler circuit and implement it in finding the values of I₁, I₂ and I₃ at t = ∞.

A capacitor of capacitance $C$ is initially uncharged and connected in series with a resistor $R$ and a battery of emf $V$. At time $t=0$, the switch is closed to begin charging the capacitor. What is the charge $q$ on the capacitor immediately after the switch is closed?

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

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?

What is the capacitance $C$ of a parallel-plate capacitor with plate area $A$, plate separation $d$, and dielectric constant $\epsilon$ between the plates?

In a simple circuit with a capacitor of charge $q$ connected between two points, if the measured voltage across the capacitor is positive when $q$ is positive, which plate is at a higher electric potential?

(II) How strong is the electric field between the plates of a 0.80-μF air-gap capacitor if they are 2.0 mm apart and each has a charge of magnitude 84-μC?

A system of four capacitors is connected such that the potential difference across points a and b is $50.0 V$. If each capacitor has a capacitance of $10.0 \mathrm{\mu F}$ and all are connected in series, what is the equivalent capacitance between points a and b?

A parallel-plate capacitor is charged and then disconnected from the battery. Which of the following changes would halve its capacitance ($C$)?

Which of the following is the correct SI unit for capacitance?

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)?