Capacitor and Inductor: Concept, Working, and Differences

Capacitor and Inductor are two fundamental passive components used in electrical and electronic circuits. Both store energy but in different forms — a capacitor stores energy in an electric field, whereas an inductor stores energy in a magnetic field. Understanding their basic concepts, working principles, applications, and key differences is essential for students preparing for SSC JE, RRB JE, GATE, and other electrical exams.

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📘 What is a Capacitor?

A capacitor is a passive electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by a non-conductive material called a dielectric.

🔍 Basic Structure:

• Two metallic plates (conductors)
• Dielectric medium (air, mica, ceramic, etc.)
  
  
  

⚙️ Working Principle:

When a voltage is applied across the plates, positive charge accumulates on one plate and negative on the other, creating an electric field between them. The capacitor resists sudden changes in voltage.

🔢 Capacitance:

The ability to store charge is measured in Farads (F).
Formula:

$$C = \frac{\varepsilon A}{d}$$

Where:

C – Capacitance
ε (Epsilon) – Permittivity of the dielectric material between the plates
A – Area of the plates
d – Distance between the plat

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🌀 What is an Inductor?

An inductor is a passive component that stores energy in the form of a magnetic field when current flows through it. It is typically made by winding a conductor (like copper wire) into a coil.

🔍 Basic Structure:

• Copper wire wound in coils
• Sometimes wound around a magnetic core to increase inductance
  
  

⚙️ Working Principle:

When current flows through the coil, it creates a magnetic field. If the current changes, the inductor opposes that change by inducing a voltage (back EMF), according to Lenz’s Law.

🔢 Inductance:

The ability to oppose change in current is measured in Henrys (H).
Formula:

$$V = L \frac{di}{dt}$$

Where:

• L – Inductance
• di/dt – Rate of change of current with respect to time

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🔄 Key Differences Between Capacitor and Inductor

Feature	Capacitor	Inductor
Energy Storage	In electric field	In magnetic field
Reacts To	Change in voltage	Change in current
Unit	Farad (F)	Henry (H)
Opposition	Resists change in voltage	Resists change in current
Current/Voltage Relation	Current (I) = Capacitance (C) × rate of change of voltage (dV/dt)	Voltage (V) = Inductance (L) × rate of change of current (dI/dt)
Used In	Filtering, timing circuits, coupling	Filters, transformers, chokes
Behavior in DC	Acts as open circuit	Acts as short circuit
Behavior in AC	Allows high-frequency signals	Blocks high-frequency signals

⚡ Applications of Capacitors

• Power factor correction
• Energy storage (like in camera flash)
• AC to DC conversion (filtering)
• Oscillator circuits
• Coupling and decoupling signals

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⚡ Applications of Inductors

• Chokes in power supplies
• Transformers
• Filters in electronic circuits
• Energy storage in SMPS
• Inductive sensors

⚖️ Ohm's Law in Capacitor and Inductor

Ohm’s Law generally states:

$$V = IR$$

Yeh resistors ke liye directly applicable hota hai. Lekin capacitors aur inductors ke liye current aur voltage ka relationship time-dependent hota hai, isliye in components ke liye modified forms use ki jaati hain.

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🔌 Ohm's Law in Capacitor

In capacitors, current depends on the rate of change of voltage:

$$I = C \frac{dV}{dt}$$

Explanation:

• I – Current flowing through the capacitor
• C – Capacitance of the capacitor
• dV/dt – Rate of change of voltage across the capacitor with respect to time

👉 Iska matlab hai ki agar voltage quickly change ho rahi ho, to current zyada hoga. Capacitor voltage change ka oppose karta hai.

Impedance of Capacitor in AC:

$$Z_C = \frac{1}{j\omega C}$$

Where $\omega = 2\pi f$, and $j$ is the imaginary unit.

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🌀 Ohm's Law in Inductor

In inductors, voltage depends on the rate of change of current:

$$V = L \frac{dI}{dt}$$

Explanation:

• V – Voltage across the inductor
• L – Inductance of the inductor
• dI/dt – Rate of change of current through the inductor with respect to time

👉 Iska matlab hai ki agar current rapidly change kare, to inductor us change ko oppose karta hai aur voltage generate karta hai.

Impedance of Inductor in AC:

$$Z_L = j\omega L$$

🧠 Summary Table: Ohm’s Law Analogy

Component	Basic Relation	Formula	AC Behavior (Reactance)
Resistor	Voltage is equal to current multiplied by resistance	Voltage = Current × Resistance (V = I × R)	Reactance does not vary with frequency (constant opposition)
Capacitor	Current is equal to capacitance multiplied by the rate of change of voltage	Current = Capacitance × Rate of change of voltage (I = C × dV/dt)	Capacitive reactance (X_C) = 1 / (Angular frequency × Capacitance) (X_C = 1 / (ω × C))
Inductor	Voltage is equal to inductance multiplied by the rate of change of current	Voltage = Inductance × Rate of change of current (V = L × dI/dt)	Inductive reactance (X_L) = Angular frequency × Inductance (X_L = ω × L)

🔋 Capacitor Charging and Discharging Concept

A capacitor doesn’t charge or discharge instantly — it takes time depending on the resistance and capacitance in the circuit. This process follows exponential behavior and is governed by a parameter called the time constant (τ = RC).

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⚡ 1. Charging of a Capacitor

Circuit:
When a DC voltage source is connected to a capacitor through a resistor, the capacitor starts storing charge on its plates.

Voltage across capacitor during charging:

$$V(t) = V_0 \left(1 - e^{-\frac{t}{RC}} \right)$$

Current during charging:

$$I(t) = \frac{V_0}{R} e^{-\frac{t}{RC}}$$

Where:

• V₀ – Supply voltage
• R – Resistance
• C – Capacitance
• t – Time
• e – Euler's number (approximately 2.718)

📝 Explanation:

• Initially, at t = 0, the voltage across the capacitor is 0, and the current is maximum, given by:
• I = V₀ / R (where V₀ is the supply voltage and R is the resistance).
• As time passes, the voltage across the capacitor increases, and the current decreases.
• After a time t = 5 × R × C, the capacitor is considered fully charged (approximately 99%).

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🔋 2. Discharging of a Capacitor

Circuit:
When the charged capacitor is disconnected from the power supply and connected across a resistor, it starts discharging.

Voltage across capacitor during discharging:

$$V(t)=V_0{e}^{-\frac{t}{R\mathrm{C}}}$$

Current during discharging:

$$I(t)=-\frac{V_0}{R}{e}^{-\frac{t}{R\mathrm{C}}}$$

📝 Explanation:

• Initially, the capacitor has full voltage V₀.
• As time passes, both the voltage across the capacitor and the current exponentially decrease.
• After a time t = 5 × R × C, the capacitor is almost completely discharged (approximately 99%).

⚡ Inductor Charging and Discharging Concept

An inductor, like a capacitor, doesn't instantly respond to changes in current or voltage. It takes time depending on the resistance and inductance in the circuit. This process also follows exponential behavior and is governed by a time constant (τ = L/R).

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🔋 1. Charging of an Inductor

Circuit:
When a DC voltage source is connected to an inductor through a resistor, the current starts increasing in the inductor.

• Voltage across inductor during charging:
  $V(t) = V_0 \left( e^{-t / (L / R)} \right)$
  

• Current during charging:
  $I(t)=\frac{V_0}{R}(1-e^{-t\mathrm{/}(L\mathrm{/}R)})$

Where:

• V₀ – Supply voltage
• L – Inductance
• R – Resistance
• t – Time
• e – Euler's number (approximately 2.718)

📝 Explanation:

• Initially, at t = 0, the current is 0, and the voltage across the inductor is maximum, given by V = V₀ (where V₀ is the supply voltage).
• As time passes, the current through the inductor gradually increases while the voltage across the inductor decreases.
• After a time t = 5 × (L / R), the inductor is considered fully charged (approximately 99%).

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🔋 2. Discharging of an Inductor

Circuit:
When the current source is removed and the inductor is connected across a resistor, the inductor starts discharging.

• Voltage across inductor during discharging:
  $V(t)=-V_0\left(e^{-t\mathrm{/}(L\mathrm{/}R)}\right)$

• Current during discharging:
  $I(t) = \frac{V_0}{R} e^{-t / (L / R)}$
  

📝 Explanation:

• Initially, the inductor has full current I₀.
• As time passes, both the current through the inductor and the voltage across it exponentially decrease.
• After a time t = 5 × L / R, the inductor is almost completely discharged (approximately 99%).