Parallel plate capacitor - class-XII
parallel plate capacitor
Questions
Choose the correct answer from the alternatives given.
The charge on a parallel plate capacitor varies as $q , = , q _0 , cos2\pi \nu t$. The plates are very large and close together (area = A, separation = d). The displacement current through the capacitor is then
- $3q _0 \, 2\pi \nu \, sin2\pi \nu t$
- $-q _0 \, 2\pi \nu \, sin2\pi \nu t$
- $4q _0 \, 2\pi \, sin2\pi \nu t$
- $5q _0 \, 2\pi \, sin2\pi \nu t$
The capacitance of a capacitor does not depend on
- the separation between the plates
- the size of the plates
- the charges on the plates
- none of the above
Three connected conductors A, B and C have a total charge of 48$\mu V$. The ratio of their capacitance are 1 :3 : 2. The charges on thei individually.
- 24$
\mu C
$
, 12$
\mu C
$
, 12$
\mu C
$ - 8$
\mu C
$
,18$
\mu C
$
,22$
\mu C
$ - 8$
\mu C
$
,24$
\mu C
$
,16$
\mu C
$ - 16$
\mu C
$
, 16$
\mu C
$
,16$
\mu C
$
A capacitor of $40\ \mu F$ charged upto $1000\ V$ is joined in parallel to another capacitor of $20\ \mu F$ charged upto $400\ V$. What is the common potential difference between the two ends of their connection ?
- $900\ V$
- $700\ V$
- $850\ V$
- $1000\ V$
Two capacitor each having a capacitance $C$ and breakdown voltage $V$ are joined in series. The effective capacitance and maximum working voltage of the combination is:-
- $2C, 2V$
- $\dfrac{C}{2}, \dfrac{V}{2}$
- $2C, V$
- $\dfrac{C}{2}, 2V$
A cylindrical capacitor has two co-axial cylinders of length $20\ cm$ and radii $2r$ and $r$. Inner cylinder is given a charge $10\ \mu F$. The potential difference between the two cylinders will be ?
- $\dfrac {0.1 \ln {2}}{4 \pi \epsilon _{0}}m\ V$
- $\dfrac {\ln {2}}{4 \pi \epsilon _{0}}m\ V$
- $\dfrac {10\ln {2}}{4 \pi \epsilon _{0}}m\ V$
- $\dfrac {0.01\ln {2}}{4 \pi \epsilon _{0}}m\ V$
If on combining two charged bodies, the current does not flow then :
- charge is equal on both
- capacitance is equal on both
- potential is equal on both
- resistance is equal on both
A condenser of capacity $ 2 \mu F$ is charged to a potential of 200V. It is now connected to an uncharged condenser of capacity $ 3 \mu F$. The common potential is :
- 200 V
- 100 V
- 80 V
- 40 V
Two connected bodies having respectively capacitances ${\text{C}} _{\text{1}} ,{\text{and}},{\text{C}} _{\text{2}} $ are charged with a total charge Q. The potentials of the two bodies are.
- $
\dfrac{{\text{Q}}}
{{{\text{C}} _{\text{1}} + C _2 }},\dfrac{Q}
{{C _1 + C _2 }}
$ - $
\dfrac{Q}
{{C _1 }} + \dfrac{{\text{Q}}}
{{C _2 }},\dfrac{Q}
{{C _1 }} + \dfrac{{\text{Q}}}
{{C _3 }}
$ - $
\dfrac{{C _1 C _2 }}
{{C _1 + C _2 }},\dfrac{{C _1 C _2 }}
{{C _1 - C _2 }}
$ - $
\dfrac{Q}
{{C _1 }} - \dfrac{Q}
{{C _2 }},\dfrac{Q}
{{C _1 - C _2 }}
$
Two capacitors A and B of capacitance $ 6 \mu F$ and $10 \mu F$ respectively are connected in parallel and this combination is connected in series with a third capacitors C of $ 4 \mu F $. A potential difference of 100 volt is applied across the entire combination. Find the charge and potential difference across $6\ \mu F$ capacitor.
- $120 \mu \, C; 20 V.$
- $200 \mu \, C; 20 V.$
- $320 \mu \, C; 80 V.$
- $320 \mu \, C; 60 V.$
A glass slab is put within the plates of a charged parallel plate condenser. Which of the following quantities does not change?
- energy of the condenser
- capacity
- intensity of electric field
- charge
Find the potential at a point due to a positive charge of $100\mu C$ at a distance of $10\ m$ in a medium of dielectric constant $9$.
- $10^{7}V$.
- $10^{4}V$.
- $10^{5}V$.
- $10^{6}V$.
A capacitor of capacitance 2 $\mu $ F is charged to a potential difference of 12 V. It is then connected across inductor of inductance 0.6 mH. The current in the circuit when the potential difference across the capacitor 6 V is :
- 3.6 A
- 2.4 A
- 1.2 A
- 0.06 A
The parallel plates of capacitor are charged to a potential difference of 320 volts and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. Alter 1 second the potential difference between the plates of the capacitor is 240 volts then after 2 seconds the potential difference between the plates will be -
- 200 V
- 180 V
- 160 V
- 140 V
When charge is supplied in a system where the capacitor are connnected in parallel. the charge will be distributed
- Equally to all the capacitor
- indirect ratio to the capacitance value
- in an inverse ratio to the capacitance values
- both (b) and (c)
Two identical capacitors are connected in parallel across a potenial difference V. after they are fully charged, the positive plate of first capacitor is connected to negative plate of second and negative plate of first is connected to positive plate of other. The loss of energy will be
- $\dfrac { 1 }{ 2 } { CV }^{ 2 }$
- ${ CV }^{ 2 }$
- $\dfrac { 1 }{ 4 } { CV }^{ 2 }$
- Zero
A simple pendulum of mass m charged negatively to q coulomb oscillates with a time period T in a downward electric field E such that mg > qE. If the electric field is withdrawn, the new time period :
- $=$T
- $>$T
- $<$T
- any of the above three is possible
Among two discs $A$ and $B$, first have radius $10\ cm$ and charge ${10}^{-6}\ \mu C$ and second have radius $30\ cm$ and charge ${10}^{-5}C$. When they are touched, charge on both ${q} _{A}$ and ${q} _{B}$ respectively will be :
- ${q} _{A}=2.75\mu C,{q} _{B}=3.15\mu C$
- ${q} _{A}=1.09\mu C,{q} _{B}=1.53\mu C$
- ${q} _{A}={q} _{B}=5.5\mu C$
- none of these
Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of mass $1.96\times 10^{-15}kg$ is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is
- 8
- 6
- 0.1
- 3
Consider two bodies A and B of same capacitance. If charge of -10C flows from body A to body B, then
- the potential of body A increases.
- the potential of body B decreases
- the magnitude of change in potential in both bodies is same.
- All the above
Which of the following is true about field between parallel charged plates?
- It is strongest between the plates
- It is strongest near the positive plate
- It is strongest near the negative plate
- The field is constant between the plates
- The field is variable, therefore the strong point also varies
A capacitor contains two square plates with side lengths $5.0$ cm. The plates are separated by $2.0$ mm. Dry air fills the space between the plates. Dry air has a dielectric constant of $1.00$ and experiences dielectric breakdown when the electric field exceeds $3.0 \times 10^4$ V/cm.
What is the magnitude of charge that can be stored on each plate before the capacitor exceeds its breakdown limit and sends a spark between the plates?
- $6.6 \times 10^{-8}C$
- $6.6 \times 10^{-5}C$
- $3.3 \times 10^{-7}C$
- $3.3 \times 10^{-84}C$
- $8.1 \times 10^{-2}C$
An air-gap parallel plate capacitor is fully charged by a battery.
What combination of two measurements will allow someone to calculate the magnitude of the electric field in between the capacitor plates?
- The potential difference of the battery and the area of the plates.
- The charge on the plates and the distance between the plates.
- The charge on the plates and the area of the plates.
- The area of the plates and the distance between the plates.
- More than two measurements are needed to calculate the electric field in between the capacitor plates.
Two capacitors of $10\ pF$ and $20\ pF$ are connected to $200\ V$ and $100\ V$ sources respectively. If they are connected in parallel by the wire, what is the common potential of the capacitors?
- $133.3\ Volt$
- $150\ Volt$
- $300\ Volt$
- $400\ Volt$
A thunder cloud and the earth's surface may be regarded as a pair of charged parallel plates separated by a distance $h$ and the capacitance of the system is $C$. When a flash of mean current '$i$' occurs for a time duration '$t$', the electric field strength between the cloud and earth is:
- $\dfrac { it }{ C } $
- $Cit$
- $\dfrac { it }{ Ch } $
- $\dfrac { Cit }{ h } $
You measure the capacitor and inductor voltages in a driven RLC circuit, and find 10V for the rms capacitor voltage and 15V for the rms inductor voltage.
- $\omega = \omega _{res}$
- $\omega < \omega _{res}$
- $\omega > \omega _{res}$
- Can't be said
The frequency for which $5\mu F$ capacitor has a reactance of $10,000 \Omega$ is
- $(100/\pi )$ cycles per second
- $(10/\pi )$ cycles per second
- $200$ cycles per second
- $5,000$ cycles per second
Two point charges $17.7 \mu c$ and $-17,7 \mu c$ separated by a very small distance, are kept inside a large hollow metallic sphere. Electric flux emnating through the sphere is :
- $ 2 \times 10^6$Vm
- $- 2 \times 10^6$Vm
- Zero
- $ 4 \times 10^6$Vm
A parallel plate capacitor has an electric field of $105$V /m between the plates .If the charge on one of the capacitor plate is 1$\mu$C,then the magnitude of the force on each capacitor plate is :
- 0. 1 N
- 0. 05 N
- 0. 5 N
- 0. 01 N
In 1909, Robert Millikan was the first to find the charge of an electron
in his now-famous oil-drop experiment. In that experiment, tiny oil
drops were sprayed into a uniform electric field between a horizontal
pair of oppositely charged plates.The drops were observed with a
magnifying eyepiece, and the electric field was adjusted so that the
upward force on some negatively charged oil drops was just sufficient to
balance the downward force of gravity. That is, when suspended, upward
force qE just equaled mg. Millikan accurately measured the charges on
many oil drops and found the values to be whole number multiples of
$1.6 \times 10^{-19} C$ the charge of the electron. For this, he won
the Nobel prize. Extra electrons on this particular oil drop (given the presently known charge of the electron) are :
- $4$
- $3$
- $5$
- $8$