Physics Tutor in Manish Nagar Nagpur – Parallel Plate Capacitor, Dielectric and Charging of Capacitor
+91-9958461445
If you are living in Physics Tutor in Manish Nagar Nagpur and Physics feels difficult, then you should connect with Kumar Sir. Kumar Sir teaches Physics in a very simple, conceptual and one-to-one style. Topics like capacitors, dielectric, electric field, potential difference, charge and energy become very easy when they are explained step by step.
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1. Parallel Plate Capacitor Derivation
A parallel plate capacitor consists of two large conducting plates placed parallel to each other. Let:
Area of each plate = A
Distance between plates = d
Charge on plates = +Q and -Q
Surface charge density = sigma
Permittivity of free space = epsilon0
Surface charge density:
sigma = Q / A
Electric field between two plates:
E = sigma / epsilon0
Now put sigma:
E = Q / (epsilon0 A)
Potential difference between plates:
V = E d
So:
V = Qd / (epsilon0 A)
Capacitance is:
C = Q / V
Now put value of V:
C = Q / [Qd / (epsilon0 A)]
So final formula:
C = epsilon0 A / d
This is the capacitance of a parallel plate capacitor without dielectric.
Kumar Sir style concept:
Capacitance increases when plate area increases and capacitance decreases when distance between plates increases. So large area and small separation give high capacitance.
2. Parallel Plate Capacitor Completely Filled With Dielectric
Now suppose a dielectric medium of dielectric constant K is completely filled between the plates.
Without dielectric:
C0 = epsilon0 A / d
With dielectric:
C = K epsilon0 A / d
So:
C = K C0
This means capacitance becomes K times.
Why does this happen?
When dielectric is inserted, its molecules get polarized. Due to polarization, the net electric field inside the capacitor decreases. For the same charge, potential difference decreases. Since capacitance is:
C = Q / V
If V decreases, C increases.
Important result:
Electric field inside dielectric = E0 / K
Potential difference with dielectric = V0 / K
Capacitance with dielectric = K C0
3. Parallel Plate Capacitor With Dielectric Slab of Thickness t
Now suppose dielectric slab of thickness t is inserted between plates, but it does not fill the complete gap.
Let:
Total distance between plates = d
Thickness of dielectric slab = t
Dielectric constant = K
Area of plates = A
The remaining air gap is:
d – t
The capacitor behaves like two capacitors in series:
Air gap of thickness d – t
Dielectric slab of thickness t
Effective separation becomes:
d effective = d – t + t / K
Therefore capacitance is:
C = epsilon0 A / [d – t + t / K]
This is very important for NEET and JEE.
Special cases:
If t = 0, then:
C = epsilon0 A / d
If t = d, then:
C = K epsilon0 A / d
So this formula covers both normal capacitor and fully dielectric-filled capacitor.
4. Parallel Plate Capacitor With Conducting Plate of Thickness t
Now suppose a conducting plate of thickness t is inserted between the plates of capacitor. The conducting plate does not touch the capacitor plates.
Inside a conductor, electric field is zero. So potential drop inside conducting slab is zero.
Only remaining air gap contributes to potential difference.
Effective separation becomes:
d effective = d – t
Therefore capacitance becomes:
C = epsilon0 A / (d – t)
Important point:
A conducting slab increases capacitance because effective distance between plates decreases.
If conducting slab thickness increases, capacitance increases.
5. Difference Between Dielectric Slab and Conducting Slab
| Case | Effective separation | Capacitance |
|---|---|---|
| No slab | d | C = epsilon0 A / d |
| Full dielectric | d / K | C = K epsilon0 A / d |
| Dielectric slab thickness t | d – t + t / K | C = epsilon0 A / [d – t + t / K] |
| Conducting slab thickness t | d – t | C = epsilon0 A / (d – t) |
Kumar Sir style shortcut:
Dielectric reduces effective thickness by factor K.
Conducting slab removes its thickness from electric field region.
6. Charging of Capacitor
When a capacitor is connected to a battery through a resistor, charging starts. Initially capacitor has no charge, so potential difference across capacitor is zero. Current is maximum at the beginning.
As charge increases on capacitor plates, potential difference across capacitor also increases. Due to this, charging current gradually decreases.
At final stage, capacitor becomes fully charged and current becomes zero.
Charging formula:
q = Q [1 – e^(-t/RC)]
Here:
q = charge at time t
Q = maximum charge
R = resistance
C = capacitance
RC = time constant
Maximum charge:
Q = CV
Voltage across capacitor during charging:
V capacitor = V [1 – e^(-t/RC)]
Current during charging:
I = I0 e^(-t/RC)
Initial current:
I0 = V / R
Time constant:
tau = RC
After one time constant, capacitor charges approximately 63 percent.
After five time constants, capacitor is almost fully charged.
7. Why Students Make Mistakes in Capacitor Questions
Students usually make these mistakes:
They forget whether battery is connected or removed.
They confuse dielectric slab with conducting slab.
They do not understand effective distance.
They memorize formulas without understanding electric field.
They do not know when charge is constant and when voltage is constant.
Kumar Sir teaches a simple rule:
If battery is connected, voltage remains constant.
If battery is removed, charge remains constant.
If dielectric is inserted, capacitance increases.
If conducting slab is inserted, effective distance decreases.
8. Why Learn From Kumar Sir?
Kumar Sir has 30 years teaching experience. He teaches Physics with concept clarity, derivation, diagrams, numericals and exam-oriented practice. He explains every formula from the basic idea so that students do not just memorize, but actually understand Physics.
In capacitor chapters, Kumar Sir focuses on:
Electric field concept
Potential difference
Capacitance derivation
Dielectric effect
Conducting slab effect
Charging and discharging
NEET numericals
JEE conceptual questions
CBSE derivations
IB, AP, IGCSE and A-Level Physics support
If you are living in Manish Nagar Nagpur and want personal Physics guidance, then Kumar Sir’s one-to-one online classes can help you build strong concepts.
नीचे चारों diagrams copy-paste friendly text format में हैं। Website पर सीधे paste कर सकते हैं।
1. Parallel Plate Capacitor Without Dielectric
Positive Plate Negative Plate
+ + + + + + + + + - - - - - - - - -
|---------------| |---------------|
| | | |
| |<------ distance d --->| |
| | | |
|---------------| |---------------|
Medium between plates = Air / Vacuum
Area of each plate = A
Charge on plates = +Q and -Q
Formula:
C = epsilon0 A / d
2. Parallel Plate Capacitor Fully Filled With Dielectric
Positive Plate Negative Plate
+ + + + + + + + + - - - - - - - - -
|---------------|=======================|---------------|
| | DIELECTRIC K | |
| |<------ distance d --->| |
| | FULLY FILLED | |
|---------------|=======================|---------------|
Dielectric fills complete space between plates
Dielectric constant = K
Area of each plate = A
Formula:
C = K epsilon0 A / d
3. Parallel Plate Capacitor With Dielectric Slab of Thickness t
Positive Plate Negative Plate
+ + + + + + + + + - - - - - - - - -
|---------------|============|----------------------|---------------|
| | DIELECTRIC | AIR GAP | |
| | K | | |
| |<--- t ---->|<------ d - t ------->| |
|---------------|============|----------------------|---------------|
Total distance between plates = d
Dielectric slab thickness = t
Remaining air gap = d - t
Dielectric constant = K
Area of each plate = A
Formula:
C = epsilon0 A / [d – t + t / K]
4. Parallel Plate Capacitor With Conducting Slab of Thickness t
Positive Plate Negative Plate
+ + + + + + + + + - - - - - - - - -
|---------------|---------|================|--------|---------------|
| | AIR GAP | CONDUCTOR | AIR GAP| |
| | | thickness t | | |
| |<-------- total distance d -------->| |
|---------------|---------|================|--------|---------------|
Conducting slab does not touch the plates
Electric field inside conductor = 0
Effective distance = d - t
Area of each plate = A
Formula:
C = epsilon0 A / (d – t)
Final Comparison Table
| Case | Formula |
|---|---|
| Parallel plate capacitor without dielectric | C = epsilon0 A / d |
| Fully filled with dielectric | C = K epsilon0 A / d |
| Dielectric slab of thickness t | C = epsilon0 A / [d – t + t / K] |
| Conducting slab of thickness t | C = epsilon0 A / (d – t) |
Final Words
If you are searching for Physics Tutor in Manish Nagar Nagpur, then Kumar Sir is the right choice for Class 11, Class 12, NEET, JEE, CBSE, IB, AP, IGCSE and A-Level Physics.
Capacitors are not difficult if you understand electric field, potential difference and charge properly. Kumar Sir teaches these topics step by step so that students can solve derivations and numericals confidently.
Call / WhatsApp: +91-9958461445
Website: Kumar Physics Classes