Concept Notes (Deep Explanation + Examples)
🔹 Introduction
In AC circuits, we often find Resistor (R), Inductor (L), and Capacitor (C) connected together.
These form the RLC circuit, one of the most important topics in ECET EEE.
Understanding RLC behavior helps in analyzing filters, power factor correction, and even motor control panels and substation systems.
Think of it like this:
- Resistor (R) → converts energy to heat → like a brake in the system.
- Inductor (L) → stores energy in a magnetic field → like a coil spring storing energy.
- Capacitor (C) → stores energy in an electric field → like a water tank storing charge.
When AC is applied, all three interact, causing phase differences between current and voltage.
🔹 Types of RLC Circuits
There are three basic configurations:
1️⃣ Series RLC Circuit
2️⃣ Parallel RLC Circuit
3️⃣ Resonance condition (special case where reactances cancel each other)
Let’s go step by step 👇
⚙️ 1. Series RLC Circuit
In a series RLC circuit, the same current flows through R, L, and C.
Total impedance:
Where:
and 
Phase angle:
Power factor (pf):
🔸 If 
→ circuit is inductive (current lags voltage)
🔸 If 
→ circuit is capacitive (current leads voltage)
🔸 If 
→ resonance → circuit purely resistive
⚙️ 2. Parallel RLC Circuit
In a parallel RLC circuit, voltage is common across each branch, but current divides.
The admittance (Y) is reciprocal of impedance:
Where:
Phase angle:
This circuit is widely used in power factor correction panels and distribution systems.
⚙️ 3. Resonance in RLC Circuit
At resonance,
or
Resonant frequency:
At this point:
- Impedance is minimum (series) or maximum (parallel)
- Current is maximum (series)
- Voltage and current are in phase
- Power factor = 1 (unity)
⚡ Practical Example:
In industrial power factor correction, capacitors are used to tune circuits close to resonance for maximum efficiency.
🧩 4. Power in AC Circuits
Instantaneous power = 
Average power = 
Reactive power = 
Apparent power = 
These form the power triangle where:
Power factor improvement is key in electrical machines and substations.
⚙️ 5. Quality Factor (Q)
Quality factor indicates how sharp the resonance is:
A high Q → narrow bandwidth → better selectivity.
Used in tuned amplifiers, filters, and resonance circuits.
🔹 Real-World Example (EEE Application)
In substations or motor control panels, RLC concepts are used:
- R → resistors in heaters or protection circuits
- L → inductors in chokes, motors, and relays
- C → capacitors in PF correction panels
A 3-phase power factor correction unit combines L and C to keep system current in phase with voltage, saving power and reducing losses.
⚙️ Formulas (Plain LaTeX Only)
🔟 10 MCQs (GATE + ECET Mixed)
1️⃣ In a series RLC circuit at resonance, the impedance is:
A) Maximum
B) Minimum
C) Zero
D) Infinite
2️⃣ The current in a series RLC circuit is maximum when:
A)
B)
C) 
D) 
3️⃣ In a purely inductive circuit, current:
A) Lags voltage by 90°
B) Leads voltage by 90°
C) In phase
D) Opposite phase
4️⃣ In a purely capacitive circuit, current:
A) Lags voltage by 90°
B) Leads voltage by 90°
C) In phase
D) None
5️⃣ Quality factor of a circuit is given by:
A) 
B) 
C) 
D) 
6️⃣ In a series RLC circuit, power factor is unity when:
A)
B)
C)
D)
7️⃣ The reactive power in a purely resistive circuit is:
A) Zero
B) Maximum
C) Minimum
D) Infinite
8️⃣ The frequency at which the current is maximum in a series RLC circuit is called:
A) Cut-off frequency
B) Resonant frequency
C) Peak frequency
D) None
9️⃣ In an inductive circuit, power is:
A) Fully consumed
B) Fully reactive
C) Half consumed
D) Negative
10️⃣ The impedance of a parallel RLC circuit at resonance is:
A) Maximum
B) Minimum
C) Zero
D) Infinite
✅ Answer Key (WordPress Table Format)
Q.No Answer
1 B
2 A
3 A
4 B
5 B
6 A
7 A
8 B
9 B
10 A
🧠 MCQ Explanations (Step-by-Step)
1️⃣ B – Minimum:
At resonance, , so impedance = R only, which is minimum.
2️⃣ A – :
Current is maximum when reactances cancel each other → resonance.
3️⃣ A – Lags by 90°:
In pure inductors, voltage leads current by 90°.
4️⃣ B – Leads by 90°:
In capacitors, current leads voltage by 90°.
5️⃣ B – 
:
Higher inductive reactance or lower resistance gives higher Q.
6️⃣ A – :
At this point, pf = 1 because current and voltage are in phase.
7️⃣ A – Zero:
No phase difference in resistive circuits → no reactive power.
8️⃣ B – Resonant frequency:
Defined by .
9️⃣ B – Fully reactive:
Inductor only stores energy → no real power, only reactive.
10️⃣ A – Maximum:
At resonance in parallel RLC, impedance becomes maximum.
🎯 Motivation / Why Practice Matters (ECET 2026 EEE)
RLC circuits are core concepts for every electrical engineer.
They appear frequently in ECET, GATE, and practical labs — from resonance tests to PF correction setups.
Mastering RLC basics helps you:
- Solve AC circuit numericals fast
- Understand machine performance
- Design power factor correction systems
- Tackle control and instrumentation questions with confidence
💡 Remember:
“Electric current follows the easiest path — success follows consistent practice.”
Keep revising, keep testing yourself daily 🔋
📲 CTA (Fixed)
Join our ECET 2026 EEE WhatsApp Group for daily quizzes & study notes:
https://chat.whatsapp.com/GniYuv3CYVDKjPWEN086X9
