Difference Between Purely Resistive, Inductive, and Capacitive AC Circuits
Purely Resistive, Purely Inductive, and Purely Capacitive Circuit are fundamental AC circuit types with unique current-voltage relationships that every JEE Main aspirant must master. These circuits serve as the baseline for understanding more advanced AC circuit concepts and composite RL, RC, and RLC circuits. Quick, accurate recognition of their behavior, formulas, and phasor diagrams is essential for problem-solving in both theory and numericals.
Each type—resistive, inductive, and capacitive—contains only one circuit element. The response to an applied alternating voltage differs distinctly. Recognizing these differences is crucial for scoring well on questions involving current electricity and AC analysis in the JEE Main syllabus.
This page offers clear definitions, governing formulas, phasor diagrams, and a thorough comparison of all three circuits. Get ready for quick revision, application-focused examples, and key traps—fully aligned with Vedantu’s high standards and JEE Main exam trends.
Definition and Behavior of Purely Resistive, Inductive, and Capacitive Circuits
A purely resistive circuit has only resistors, showing no phase difference between voltage and current. In a purely inductive circuit, only inductors are present—current lags voltage by exactly 90°. A purely capacitive circuit contains only capacitors, where current leads voltage by 90°. These relationships help quickly identify circuit types in questions.
- Resistive: current and voltage in phase, power consumed.
- Inductive: current lags behind voltage, power alternates, average zero.
- Capacitive: current leads voltage, power alternates, average zero.
Mastering these basics supports solving complicated AC networks and understanding phase differences—core for both subjective and MCQ problems in JEE Physics.
Standard Formulas and Mathematical Representation of Purely Resistive, Inductive, and Capacitive Circuit
The formulas below form the backbone for calculating circuit responses. Know their symbols and conditions for direct application in JEE questions.
| Type | Main Law/Formulas | Impedance | Phase Angle (φ) |
|---|---|---|---|
| Resistive | V = V0sin(ωt), I = I0sin(ωt) | R | 0° |
| Inductive | V = V0sin(ωt), I = I0sin(ωt – 90°) | ωL | +90° |
| Capacitive | V = V0sin(ωt), I = I0sin(ωt + 90°) | 1/ωC | –90° |
Here, V0 is the peak voltage, I0 is the peak current, ω is angular frequency, L is inductance, C is capacitance, and R is resistance. Getting the impedance and phase right makes solving reactance questions easy.
Phasor Diagrams for Purely Resistive, Inductive, and Capacitive Circuit
Phasor diagrams are graphical tools representing amplitude and relative phase of voltage and current. For JEE, always draw the reference axis clearly. Note how the phase angle distinguishes each circuit type.
- Resistive: Voltage and current vectors are colinear (0° phase).
- Inductive: Voltage leads current by 90°; current vector lags below.
- Capacitive: Current leads voltage by 90°; current vector ahead.
Drawing correct phasors is tested in both theory and MCQ-style questions. This skill also helps when solving RL circuit and RC circuit questions on the JEE exam.
Comparison Table: Purely Resistive, Inductive, and Capacitive Circuit
| Aspect | Resistive | Inductive | Capacitive |
|---|---|---|---|
| Voltage-Current Phase | In phase | Voltage leads by 90° | Current leads by 90° |
| Impedance | R | ωL | 1/ωC |
| Power Factor | 1 (maximum) | 0 | 0 |
| Average Power | Consumed | Zero | Zero |
| Energy Storage | No | In magnetic field | In electric field |
Examples and Applications of Purely Resistive, Inductive, and Capacitive Circuit
Quick examples help identify these circuits in real JEE questions:
- A glowing bulb in AC acts as a pure resistor.
- An ideal inductor in AC is modeled by a coil with no resistance (inductor circuit).
- A good air-filled capacitor connected across AC supply is almost purely capacitive.
- Transformers use the properties of pure inductance for energy transfer.
- Pulsed charging circuits use near-pure capacitance for energy storage buffers.
These behaviors get tested in conceptual problems and calculation-based questions, especially where you must calculate phase, average power, or reactance.
Numerical Example: Purely Resistive, Purely Inductive, and Purely Capacitive Circuit in Practice
A 20 V, 50 Hz AC source is connected across:
- 1: a 10 Ω resistor
- 2: a 200 mH inductor
- 3: a 50 μF capacitor
- For resistor: I = Vrms/R = 20/10 = 2.0 A
- For inductor: XL = ωL = 2π×50×0.2 = 62.83 Ω
I = 20/62.83 = 0.318 A - For capacitor: XC = 1/(ωC) = 1/[2π×50×50×10-6] = 63.66 Ω
I = 20/63.66 = 0.314 A
Notice the different current values, all for the same voltage. The difference is due to the circuit type—key point on the JEE Main.
Common Mistakes and JEE Tips for Purely Resistive, Purely Inductive, and Purely Capacitive Circuit
- Confusing “leading” vs “lagging”—memorize: inductor lags, capacitor leads.
- Forgetting power factor—neutral for resistors, zero for ideal L or C in AC.
- Assuming real components are always ideal—true only for conceptual numericals.
- Misreading ω (use rad/s, not Hz).
- Dismissing differences between inductive and capacitive behavior in trick questions.
Continuing with strong fundamentals and careful analytical habits boosts exam results. Use revision sheets and Vedantu revision notes for the last mile.
A strong grasp of purely resistive, purely inductive, and purely capacitive circuit unlocks understanding of all AC network questions for JEE Main. Practice with genuine examples and refer to the theory whenever you see phase, impedance, or true/reactive power in the question.
For more clarity, you can review topics such as inductive and capacitive reactance, Kirchhoff's laws, and difference between resistance and impedance, all interlinked at Vedantu for your seamless exam preparation journey.
FAQs on Purely Resistive, Inductive, and Capacitive Circuits: Concepts, Formulas & Phasor Diagrams
1. How do you know if a circuit is purely resistive, inductive, or capacitive?
Purely resistive, inductive, or capacitive circuits can be identified by their components and current-voltage phase relationships:
- Purely Resistive: Only resistors present; current and voltage are in phase.
- Purely Inductive: Only inductors present; current lags voltage by 90°.
- Purely Capacitive: Only capacitors present; current leads voltage by 90°.
2. What is the current-voltage phase relationship in purely resistive, purely inductive, and purely capacitive circuits?
The current-voltage phase relationship differs in each circuit type:
- Purely Resistive Circuit: Current and voltage are in phase (0° phase difference).
- Purely Inductive Circuit: Current lags voltage by 90° (π/2 radians).
- Purely Capacitive Circuit: Current leads voltage by 90° (π/2 radians).
3. What are the formulas for purely resistive, purely inductive, and purely capacitive circuits?
Standard formulas for current in each circuit are:
- Purely Resistive: I = V/R
- Purely Inductive: I = V/(ωL), where ω is angular frequency and L is inductance.
- Purely Capacitive: I = V/(1/ωC) = V·ωC, where C is capacitance.
4. How do phasor diagrams differ for purely resistive, inductive, and capacitive circuits?
Each phasor diagram visually represents the phase difference:
- Purely Resistive: Voltage and current phasors overlap (same direction).
- Purely Inductive: Voltage leads current by 90° (V phasor ahead of I).
- Purely Capacitive: Current leads voltage by 90° (I phasor ahead of V).
5. What is the difference between purely resistive, inductive, and capacitive circuits?
Purely resistive, inductive, and capacitive circuits differ in components, phase relationship, and power consumption:
- Resistive: Current and voltage are in phase; true power is consumed (P = VI).
- Inductive: Current lags voltage by 90°; average power consumed is zero.
- Capacitive: Current leads voltage by 90°; average power consumed is zero.
6. Can you give real-life examples of purely resistive, inductive, and capacitive circuits?
Real-world examples help relate AC circuit theory to practical cases:
- Purely Resistive: Electric heaters, incandescent bulbs (mainly resistors).
- Purely Inductive: Ideal coils, transformer windings (in theory).
- Purely Capacitive: Isolated capacitor circuits, tuning circuits in radios.
7. Does power consumption differ between purely resistive, inductive, and capacitive circuits?
Power consumption varies in each type:
- Resistive: Consumes real power (P = VI), power factor = 1.
- Inductive & Capacitive: Average power consumed is zero (P = 0), as energy is alternately stored and released but not dissipated.
8. Can a real circuit ever be perfectly resistive, inductive, or capacitive?
In practice, perfectly pure circuits do not exist as all real components have some resistance, inductance, or stray capacitance.
- Purely resistive, inductive, or capacitive circuits are theoretical models used for analysis and ideal scenarios in exams.
- Real loads are close to pure type, but never exactly so.
9. What formula is used for purely inductive and purely capacitive AC circuits?
For AC circuits with only inductance or capacitance:
- Purely Inductive: I = V/(ωL), where ω = 2πf and L is inductance.
- Purely Capacitive: I = V·ωC, where C is capacitance.
10. Why don't capacitive and inductive circuits consume true power in an AC cycle?
Purely inductive and purely capacitive circuits do not consume real power in AC because the average power over a cycle is zero:
- Energy is alternately stored in the magnetic field (inductor) or electric field (capacitor) and then returned to the source.
- Current and voltage are 90° out of phase; thus, real power (P = VI cos φ) equals zero, as cos 90° = 0.
