26. Capacitors & Dielectrics

A large metal sheet of thickness ℓ is placed between, and parallel to, the plates of the parallel-plate capacitor of Fig. 24–4. It does not touch the plates, and extends beyond their edges. If ℓ = 0.40 d, by what factor does the capacitance change when the sheet is inserted?

What is the capacitance of the two metal spheres shown in FIGURE EX26.22?

(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 = ∞.

Determine the capacitance of the Earth, assuming it to be a spherical conductor.

What is the capacitance of a pair of circular plates with a radius of 5.0 cm separated by 2.3 mm of mica?

A circuit contains three capacitors: $C=2\mu F$ and $C=4\mu F$ are connected in series, and this combination is connected in parallel with a $C=6\mu F$ capacitor. What is the equivalent capacitance of the entire combination?

A $4.0\mu F$ capacitor is connected to a $12V$ battery. What is the charge stored on the capacitor?

In a circuit with a battery of emf $V$ and a capacitor of capacitance $C$ connected in series with a resistor, in the steady state, what is the charge $q$ on the capacitor?

A parallel plate capacitor has circular plates of radius $R$ separated by a distance $d$. If the space between the plates is filled with vacuum, what is the capacitance of the capacitor?

A capacitor of capacitance $C$ is connected in series with a resistor $R$ and a battery of emf $V$. The capacitor is initially uncharged. What is the charge $q$ on the capacitor immediately after the switch is closed?

A capacitor in a circuit (see figure 1) is initially uncharged. At time $t=0$, the switch is closed, connecting the capacitor $C$ in series with a resistor $R$ and a battery of emf $V$. Which expression gives the charge $q$ on the capacitor as a function of time $t$ after the switch is closed?

A parallel-plate capacitor is charged by a $20.0 V$ battery, then the battery is removed. What happens to the charge and voltage on the capacitor if the plate separation is doubled while it remains isolated?

In a circuit containing a charged $C$ (capacitor) and a switch, what happens to the charge on the $C$ immediately after the switch is thrown to connect the $C$ to a $R$ (resistor)?

When a charged capacitor is connected across a resistor by throwing a relay to the normally open ($n.o.$) position, how does the charge $q$ on the capacitor change with time?

For a parallel-plate capacitor, the capacitance is independent of which of the following quantities?