Question

Two parallel-plate capacitors *C*_{1} and
*C*_{2} are connected in series to a battery. Both
capacitors have the same plate area of 3.40 cm^{2} and
plate separation of 2.65 mm. However, the first capacitor
*C*_{1} is filled with air, while the second
capacitor *C*_{2} is filled with a dielectric that
has a dielectric constant of 3.40. The total charge on the series
arrangement is 13.8 pC.

(a) What is the battery voltage?

V

(b) What is the potential difference across each capacitor?

Δ |

Δ |

Answer #1

Since the capacitors are in series, the total charge on each
capacitor is same.

Consider Q be the charge on each capacitor, 2Q = 13.8 pC

Q = 6.9 pC

Capacitance of a capacitor can be written as C = KoA/d

Where K is the dielectric constant, o is the vacuum
permittivity, A is the area of the metal plates and d is the
separation between the metal plates.

A = 3.4 x 10^{-4} m^{2}.

d = 2.65 x 10^{-3} m

C1 = [**1** x (8.85 x 10^{-12}) x (3.4 x
10^{-4})] / (2.65 x 10^{-3})

= 1.1355 pF

Similarly,

C2 = [**3.4** x (8.85 x 10^{-12}) x (3.4 x
10^{-4})] / (2.65 x 10^{-3})

= 3.86 pF

V1 = Q/C1

= (6.9 pC) / (1.1355 pF)

= 6.08 V

V2 = Q/C2

= (6.9 pC) / (3.86 pF)

= 1.79 V

Voltage of the battery = 1 + V2

= 7.86 V

Two identical capacitors C1 and C2 are
connected in series with a battery with voltage V. A dielectric is
inserted between the plates of C2.
A) Does inserting the dielectric increase or decrease the
capacitance of C2? Explain.
B) Does inserting the dielectric increase or decrease the
equivalent capacitance of the two capacitor system? Explain.
C) Is there more charge on the capacitors before or after the
dielectric is inserted? Explain.
D) Which system has a larger potential drop across...

Two capacitors, C1=5900pF and C2=2600pF, are connected in series
to a 15.0 V battery. The capacitors are later disconnected from the
battery and connected directly to each other, positive plate to
positive plate, and negative plate to negative plate. What then
will be the charge on each capacitor?

Which of the following capacitors have the smallest charge?
Select a parallel plate capacitor
with an area of 10 cm2 and a plate separation of 2 mm connected to
a 10-V battery as your answer
a parallel plate capacitor with an area of 10 cm2 and a plate
separation of 2 mm connected to a 10-V battery
Select a parallel plate capacitor
with an area of 5 cm2 and a plate separation of 1 mm connected to a
10-V battery...

Capacitor C1 = 10.0 micro F is connected in series to parallel
combination of capacitors C2=7.0 microF and C3=8.0 microF. This
circuit is connected to a battery delivering V=15.0 V. Find charge
stored in capacitor C2 in mircoC.

A battery is connected purely in parallel to three capacitors of
C1 = 6 micro-farads, C2 = 9 micro-farads, and
C3 = 11 micro-farads. Then, one additional capacitor of
8 micro-farads is added in parallel to the other three capacitors
and due to this, the total stored energy of all the capacitors
increases by 196 micro-joules (it is 196 micro-joules larger with
four capacitors compared to with three capacitors). Then, the same
four capacitors are connected in SERIES to the...

Two air-filled parallel-plate capacitors (C1 and C2) are placed
in series. Both capacitors have the same plate area, but the
distance between the plates of C1 is twice the distance between the
plates of C2. If C1 is equal to 10 μF (microfarads), calculate the
equivalent capacitance Ceq of the two capacitors. Quote your answer
in μF (microfarads) rounded to one decimal place.

1. Three capacitors are connected in series and give an
effective capacitance of 22 nF. If C1 = 5 µF and C3 = 100 nF, what
is C2? Suppose V1 = 5 V. Find the charge on and voltage across the
other two capacitors. Again, calculate energy stored.
2. A parallel plate capacitor has plates with area 10 cm2 and a
gap of 2 mm. First, find the capacitance of this capacitor. Now,
imagine a metal plate of thickness 0.25...

Three parallel plate capacitors are connected in series. These
capacitors have identical geometries. However, they are filled with
three different materials. The dielectric constants of the
materials are 8.69, 8.06, and 8.68. It is desired to replace this
series combination with a single parallel plate capacitor. Assuming
that this single capacitor has the same geometry as each of the
other three capacitors, determine the dielectric constant of the
material with which it is filled

Capacitor C1=4.0 microF is connected in parallel to the series
combination of capacitors C2=13.0 microF anf C3=14.0 microF. This
combination if connected to a battery of V=15.0 V. Find potential
difference on capacitor C3.

Now let’s look at a specific problem involving series and
parallel combinations of capacitors. Two capacitors, one with
C1=6.0μF and the other with C2=3.0μF, are connected to a potential
difference of Vab=18V. Find the equivalent capacitance, and find
the charge and potential difference for each capacitor when the two
capacitors are connected (a) in series and
(b) in parallel.
PART A: Repeat this example
for Vab=18V and C1=C2=10μF. What is the equivalent
capacitance for the capacitors when they are connected in...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 16 minutes ago

asked 22 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago