# 04a - Capacitor (Problems) - Answer

```Physics
12
12 / PHYSICS
Capacitors
Worksheet : Capacitors (Problems)
CAPACITORS (Problems)
1.
1.
2.
2. 3.
A capacitor is connected to the terminals of a battery as
shown in the figure.
A Two
capacitor
is charged
and disconnected
batteryC1
capacitors
are arranged
as shown.from
The the
capacitor
ashas
shown
in theof
figure.
a charge
20µC and the capacitor C2 is uncharged.
The switches S1 and S2 are closed at the same time.
After a dielectric is inserted between the plates of
capacitor;
After a dielectric is inserted between the plates of
capacitor;
increases
a) The capacitance of capacitor ______________.
remains the same
b) Potential difference across the plates _____________.
increases
c) Charge of capacitor ______________.
increases
a)Calculate;
The capacitance of capacitor ______________..
a) final charges of each capacitor.
b) the potential difference across the plates of each
decreases
b) Potential
difference across the plates _____________.
capacitor.
c) the energy stored in the capacitor C1.
remains the same
c) Charge of capacitor ________________.
decreases
d) The electric field between the plates _____________.
1
remains the same
d) The electric field between the plates ____________.
4.
c) Charge of capacitor ______________.
DEMIC YEAR
PHYSICS
Capacitors
S (Problems)
d) The electric field between the plates ____________.
Physics
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3.
3.
Worksheet : Capacitors (Problems)
4.
Two capacitors are arranged as shown. The capacitor C1
has a charge of 20µC and the capacitor C2 is uncharged.
The switches
S1 and S2 are closed at the same time.
2.
4.
A capacitor is charged and disconnected from the battery
as shown in the figure.
For the circuit given calculate
a) Equivalent capacitance of the system
b) Total charge of the system
c) The charge of the each capacitor
d) Potential difference across the plates of each
capacitor.
After a dielectric is inserted between the plates of
Calculate;
capacitor;
a) final charges of each capacitor.
b) the potential difference across the plates of each
a) The capacitance of capacitor ______________..
capacitor.
c) the energy stored in the capacitor C1.
a) Ceq=2 µF
difference across the plates _____________.
a) b)QPotential
total=20 µC
b) Qtotal=24 µC
Q/1=5 µC and Q/2=15 µC
c) Charge of capacitor ________________.
The electric
b) d)V=5/3
voltsfield between the plates _____________.
4.
c) E=(CV2)/2=(3.(5/3)2)/2=25/6 µJ
1
c) Q1= Q2=24 µC
d) V1=8 V and V2=4 V
Physics
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Worksheet : Capacitors (Problems)
Capacitors
5.
5.
6.
6.
7.
The potential difference across the plates of C1 is 40
volts.
After the capacitors are fully charged an insulator with
K=2 is inserted between the plates of C1 and the system
is again fully charged.
Calculate;
a) The potential difference of C2
b) The potential difference of battery
c) The total charge of system
For the given circuit, calculate
a) The equivalent capacitance and the total charge of
the system.
a) What
is change in the charge of C1?
c)What
The potential
across
b)
is changedifference
in the potential
ofeach
C1? capacitor.
d) The charge stored on each capacitor.
e) The electric potential energy of the system.
a) Ceq= 2 F
a) Q1= Q2=120 C then
V2=(120)/(6)=20 V
Q1= Q2=12 C then
After dielectric is inserted;
C/1=6 F then C/eq= 3 F
b) V=40+20=60 V
c) Ceq= 2 F and V=60 V
Qtotal=2.60=120 C
6.
After the capacitors are fully charged an insulator with
Q/1= Q/2=18 C
b) V1=4 V and V2=8 V
After dielectric is inserted;
8.
V/1=3 V and V/2=3 V
After the capacitors are fully charged an insulator having
Physics
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Worksheet : Capacitors (Problems)
Capacitors
7.
7.
6.
8.
8.
After the capacitors are fully charged an insulator with
K=2 is inserted between the plates of C1 and the system
is again fully charged.
For the given circuit, calculate
a) The equivalent capacitance and the total charge of
the system.
Theispotential
difference
across
capacitor.
a) c)
What
change in
the charge
of C1each
?
Theischarge
stored
each capacitor.
b)d)
What
change
in theon
potential
of C1?
e) The electric potential energy of the system.
a) Ceq= 1+2=3 µF
Qtotal= 12.3 =36 µC
After the capacitors are fully charged an insulator having
a dielectric constant K=2 is inserted between the plates
of C1 and the system is again fully charged.
a) What is change in the charge of C1?
b) What is change in the potential of C1?
c) How does the charge of C2 change? Why?
a) Q1= 3.12=36 µC
b) V1= V2=12 V
C1= 3 µF then
c) Q1= 1.12 =12 µC
C/1= 6 µF (with dielectric)
Q2= 2.12 =24 µC
d) Etotal=CV2/2=(3.122)/2
8.
Etotal=216 µJ
After the capacitors are fully charged an insulator having
Q/1= 6.12=72 µC
b) V1= V/1=12 V
c) Q2= Q/2=48 µC
Physics
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Worksheet : Capacitors (Problems)
Capacitors
9.9.
10.
10. 11.
When
the switch
is open
the
totalthe
charge
of the syste
When
the switches
S1Sand
S2 are
open,
equivalent
is Q1. When
switch
closed the total charge of the
capacitance
of thethe
circuit
is 6isµF.
system becomes Q2.
For the circuit given, Calculate
a) charge stored on each capacitor
b) potential difference across each capacitor
c) energy stored in C2
the ratio capacitance
of Q1/ Q2? of the circuit
WhatCalculate
is the equivalent
when both switches are closed?
When both switches are open
a)
2 F and 4 F are parallel : 6 F
Ceq=C =6 µF
6 F and 12 F are series : Ceq= 4 µF then
Qtotal=4.12=48 µC
Q1=48 µC, Q2=16 µC and Q3=32 µC
When both switches are closed
b) V1=4 V and V2=V3=8 V
Ceq=10C/3
c) E2=(2.82)/2=64 J
10.
When the switches S1 and S2 are open, the equivalent
12.
Ceq=(10.6)/3=20 µF
Physics
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Worksheet : Capacitors (Problems)
Capacitors
11.
11.
10.
When the switch S is open the total charge of the system
When
the switches S1 and S2 are open, the equivalent
is Q1. When the switch is closed the total charge of the
capacitance of the circuit is 6 µF.
system becomes Q2.
12.
12.
Calculate the equivalent capacitance between points
K and L.
Calculate the ratio of Q1/ Q2?
What is the equivalent capacitance of the circuit
when both switches are closed?
S is open;
4 F and 4 F are series
Ceq=2 F then Q1=2.V
Q1/Q2=(2.V)/(8.v/3)
Q1/Q2=3/4
S is closed;
4 F and 4 F are paralle:8 F
Ceq=8/3 F then Q2=8.V/3
12.
Ceq=4+4+12
Ceq=20 F
Physics
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Worksheet : Capacitors (Problems)
Capacitors
13.
13.
15.
14.
14.
A 40 µF capacitor is charged by connecting it to 16 V
battery. The battery is then disconnected and the
charged capacitor is next connected across a 120 µF that
was initially uncharged.
After steady state has been reached, what is the
charge on each capacitor and the voltage across
each?
If the potential difference between the ends of 3µF
capacitor is 24 V, what is the potential difference
between points K and L?
What is the equivalent capacitance between th
points
K and L?
Initially;
Qi=40.16=640 µC
then
Qtotal=640 µC
Q1=160 µC and Q2=480 µC
(Q is directly proportional to C
when two capacitors are parallel.)
6.V=3.24
VKL=12+24
V=12 V
VKL=36 V
Vcommon=160/40=4 V
4
Physics
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Worksheet : Capacitors (Problems)
Capacitors
15.
15.
.
16.
16.
40 µF capacitor is charged by connecting it to 16 V
ttery. The battery is then disconnected and the
arged capacitor is next connected across a 120 µF that
as initially uncharged.
ter steady state has been reached, what is the
harge on each capacitor and the voltage across
ch?
The potential difference between the two ends of 12 µF
capacitor is 40 V.
What is the equivalent capacitance between the
points K and L?
What is the amount of charge stored in the 6µF
capacitor, in µC?
12 µF and 3 µF : parallel: 15 µF
6 µF and 4 µF : parallel: 10 µF
10 µF and 15 µF : series
8 F and 24 F : series : 6 F
6 F and 18 : parallel : 24 F
24 F and 12 F : series : Ceq=8 F
Their charges are the same.
40.15=V.10 then V=60 V
The charge on 6 µF capacitor is
Q=6.60=360 µC
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