Capacitance of conductor depends upon shape, size, presence of medium and nearness of other conductor.
Capacitors find extensive applications across diverse fields because of their efficient capability to store and discharge electrical energy. Some of the applications include Filtering and Smoothing, Energy Storage, Timing Circuits, etc.
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Parallel Plate Capacitor Questions
Parallel plate capacitors are essential components in understanding electrostatics and energy storage. These questions cover key principles such as capacitance, electric fields, dielectric effects, and potential difference, helping build a solid foundation in physics. Parallel plate capacitors are widely used in electronics and physics applications. These questions help you understand how they function, how their capacitance changes with geometry and materials, and how to apply formulas effectively.
1.0Concept of Capacitors
A capacitor or condenser consists of two conductors separated by an insulator or dielectric. Having equal and opposite charges on which sufficient quantity of charge may be accommodated.
It is a device which is used to store energy in the form of an electric field by storing charge. Conductors are used to form capacitors.
2.0Electrical Capacitance
It demonstrates a conductor's ability to store electrical energy through an electric field. If charge(Q) is given to an isolated conducting body and its potential increases by V, then Q∝V,Q=CV
⇒C=VQ(C = Capacitance of the capacitor)
Electrical capacitance is a Scalar quantity.
Capacitance of conductor depends upon shape, size, presence of medium and nearness of other conductor.
3.0Graph Between Q and V
S I Unit- Farad
CGS Unit-Stat Farad
Dimensional Formula-[M-1L-2T4A2]
4.0Circuit Symbols of Capacitor
5.0Capacitors Applications
Capacitors find extensive applications across diverse fields because of their efficient capability to store and discharge electrical energy.
Filtering and Smoothing
Energy Storage
Timing Circuits
Motor Starters
Power Factor Correction
Memory Backup
6.0Parallel Plate Capacitor(PPC)
It consists of two large plane parallel conducting plates separated by small distance
C=dϵ0A
Capacitance of parallel plate capacitor with dielectric, C=dϵrϵ0A=ϵrC0(∵C0=dϵ0A)
Capacitance of Parallel Plate Capacitor Depends on
Area C ∝ A
Distance between the plates ⇒C∝d1
Medium between the Plates ⇒C∝ϵr
7.0Capacitance of Parallel Plate Capacitor when Dielectric is Partially Filled
Capacitance is given by,
C=(d−t)+ϵrtϵ0A
8.0FAQ on Parallel Plate Capacitor Questions
Q-1.A small parallel plate capacitor has its plates charged as shown. A particle with charge q is placed at a distance l from the capacitor (where l≫d, the separation between the plates). What is the magnitude of the force acting on the charged particle due to the capacitor?
Solution:
The two plates acts as a dipole
The magnitude of force on charge q
F=∣E∣q=(r32kqd)q=2πϵ0l3qad
Q-2.A parallel plate capacitor with plate area A and plate distance d is charged to a potential difference V, after which the battery is disconnected. What is the work done in increasing the separation between the plates to 2d?
Solution: As the battery is disconnected, charge remains constant in the work process.
Work done = final potential energy – initial potential energy
Q-3.Two capacitors of capacitance 1 F and 2Fare charged to potential difference 20Vand 15V as shown in figure. If now terminal B and C are connected together terminal A with positive battery and D with negative terminal of battery 30 V then find out final charges on both the capacitors.
Solution:
Now applying Kirchoff voltage law,
−120+q−230+q+30=0
−40−2q−30−q=−60
3q=−10⇒q=−310μC
Charge flow=−310,μC
Chargeoncapacitorofcapacitance1μF=20+q=350μC
Chargeoncapacitorofcapacitance2μF=30+q=380μC
Q-4.Find out equivalent capacitance between A and B. (take each plate Area = A)
Q-5.Find out equivalent capacitance between A and B.
Solution:
Let charge distributions on plates as shown:
C=VQ=VABx+y
Potential of 1 and 4 is same:
Aϵ0y=Aϵ02x⇒y=2x
V=(Aϵ02y+x)d
C=(5x)d(x+2x)Aϵ0=5d3Aϵ0
Q-6.In a parallel plate capacitor setup, the lower plate is fixed on a rigid support, while the upper plate is suspended from one arm of a balance. Initially, the plates are connected with a thin wire and then disconnected after achieving the same potential. The balance is counterpoised at this stage. A voltage of V=5000V is then applied across the plates. The separation between the plates is d=5 mm , and the area of each plate is A=100cm2 . Assuming all components except the plates are massless and non-conducting, calculate the additional mass that must be placed on the other side of the balance to restore equilibrium.
Solution: The electric force between the plates will be balanced by the additional weight
mg=2Aϵ0Q2=2Aϵ0C2V2
mg=2d2ϵoAV2
m=2d2gϵoAV2=2×(5×10−4)3×10ϵo×100×10−4×(5000)2
m=4.425g
Q-7.One plate of a capacitor is unchanged and the other is connected to a spring as shown in Fig. The area of both the plates is A. In steady state (equilibrium), separation between the plates is 0.8 d (spring was unstretched and the distance between the plates was d when the capacitor was uncharged). The force constant of the spring is approximately.
Solution:
mg=2Aϵ0Q2=K(0.2d)
2Aϵ0(0.8dϵ0AE)2=0.2Kd
K=d33.9ϵ0AE2
Q-8.Three dielectric slabs are inserted between the plates of a parallel plate capacitor of plate area A , as shown in the figure.
Slab 1: Dielectric constant K1, area A1, thickness d
Slab 2: Dielectric constant K2, area A2, thickness d1
Slab 3: Dielectric constant K3, area A2, thickness d2
The total distance between the capacitor plates is d=d1+d2. Find the equivalent capacitance between points A and B.
Q-9.Two dielectric slabs with dielectric constants K1andK2, and thicknesses d1andd2respectively, are inserted between the plates of a parallel plate capacitor. Each slab fully covers the plate area A, and the total separation between the plates is d1+d2 . Determine the equivalent capacitance between points A and B.
Q-10.If potential of A is 5V, then potential of B in volt is
Solution:
1(8−VB)+1(8−VB)+1(5−VB)=0
21=3VB
VB=7V
Q-11.An isolated parallel plate capacitor consists of two metallic plates, each of area A , separated by a distance d . A dielectric slab of width t and dielectric constant K is inserted between the plates such that its faces are parallel to the plates and its surface area matches that of the plates.
Determine the capacitance of the system with the dielectric slab partially filling the space.
If K=2, find the ratio dt for which the capacitance becomes 23 times that of the same capacitor when it is completely filled with air.
Assuming the charge q on the plates remains constant, calculate the ratio of the electrostatic energy stored in the two cases (with and without the dielectric slab). Also, explain the physical reason for any change in energy.
Solution:
C′=d−t+ktAε0
With dielectric, C′=d−t+ktAε0=23C=23dε0A⟹td=23