Inductive Reactance vs Capacitive Reactance: Key Differences, Formula, and Applications
Inductive Reactance And Capacitive Reactance are crucial concepts in the analysis of AC circuits for JEE Main. Both describe the frequency-dependent opposition to current: inductive reactance by inductors, capacitive reactance by capacitors. Mastering their formulas, differences, and applications is vital for solving typical JEE numerical and conceptual problems involving AC circuits.
In an alternating current system, resistances alone cannot account for how current and voltage behave. Here, reactance comes in—specifically, inductive reactance (XL) for coils/inductors and capacitive reactance (XC) for capacitors. Unlike resistance, these reactances vary with frequency. Understanding this gives you a clear edge in exams.
Let's first define each one. Inductive reactance is the property of an inductor to oppose changes in current in an AC circuit. Capacitive reactance is the property of a capacitor to oppose changes in voltage in an AC circuit. Their frequency dependence is why they have a major role in filtering, resonance, and tuning applications in electrical circuits.
Formulae, Units, and Dimensional Analysis of Inductive Reactance And Capacitive Reactance
The standard formulas are essential for quick application and problem-solving. Both share the same SI unit as resistance—ohm (Ω), but their behavior in circuits is very different from a simple resistor.
| Quantity | Symbol | Formula | SI Unit | Dimension |
|---|---|---|---|---|
| Inductive Reactance | XL | 2πfL | Ω | M1L2T-3A-2 |
| Capacitive Reactance | XC | 1/(2πfC) | Ω | M1L2T-3A-2 |
XL increases with frequency (f) and inductance (L), while XC decreases as frequency or capacitance (C) increases—opposite dependencies that lead to interesting effects in circuits.
Comparing Inductive Reactance And Capacitive Reactance: Key Differences
Distinguishing between these two forms of reactance is a common JEE Main question. See their properties, formulas, and phase relationships laid out clearly:
| Factor | Inductive Reactance | Capacitive Reactance |
|---|---|---|
| Symbol | XL | XC |
| Formula | 2πfL | 1/(2πfC) |
| Frequency Dependence | Directly proportional to f | Inversely proportional to f |
| Phase | Current lags voltage by 90° | Current leads voltage by 90° |
| Nature of Opposition | Opposes change in current | Opposes change in voltage |
| At f = 0 (DC) | XL = 0, acts as a wire | XC = ∞, blocks DC |
These contrasts are critical in circuits like the RL circuit or the RC circuit, and especially in resonance and filtering topics tested in JEE.
Frequency Dependence and Graphs of Inductive Reactance And Capacitive Reactance
Visualising how reactance changes with frequency is a powerful memory tool. For inductive reactance, the graph of XL versus frequency is a straight line passing through the origin—steeper for larger L. In contrast, capacitive reactance yields a rectangular hyperbola, decreasing rapidly as f increases.
In phasor diagrams, XL always shifts current behind voltage, while XC brings current ahead. This is why in circuits with both, total reactance can be positive, negative, or zero (leading to resonance). For these graphical analyses, review AC theory and mock questions to practice frequency-based numerical problems.
Numerical Example: Applying Inductive Reactance And Capacitive Reactance Formulas
Suppose an AC circuit has a 0.10 H inductor and a 20 μF capacitor, both connected to a 50 Hz supply. Calculate XL, XC, and net reactance.
- Inductive Reactance: XL = 2πfL = 2 × 3.14 × 50 × 0.10 = 31.4 Ω
- Capacitive Reactance: XC = 1/(2πfC) = 1/(2 × 3.14 × 50 × 20 × 10-6) ≈ 159 Ω
- Total Reactance: X = XL – XC = 31.4 – 159 = –127.6 Ω (net capacitive)
A negative result shows capacitive dominance—current leads voltage. At resonance, XL=XC, so net reactance is zero and the circuit behaves purely resistive. Such cases are tested directly in JEE Main questions on LCR circuits and resonance points.
Make sure to remember that reactance, although like resistance in units, is always frequency-dependent. Always check the supply frequency, component values, and configuration before substituting in the XL or XC formulas in any calculation.
Applications and Quick Revision: Inductive Reactance And Capacitive Reactance in Real Circuits
Reactance concepts are everywhere: in tuning radios, building filters, or understanding transformers. In JEE Main, expect both direct calculation and conceptual problems using these definitions. Important applications include:
- Phase control and filtering in AC circuits
- Setting resonance conditions in RL, RC, and LCR circuits
- Impedance matching and minimizing power loss in practical circuits
- Making or breaking DC/AC current flows in inductors and capacitors
Pitfalls include forgetting the frequency effect, using wrong units, or ignoring phase differences. Always pay close attention to component arrangement and AC source parameters when tackling JEE questions on inductive reactance and capacitive reactance.
To quickly revise, remember: Inductive Reactance (XL) = 2πfL; Capacitive Reactance (XC) = 1/(2πfC). Both oppose AC, but the details of their variation with changing frequency are key to mastering JEE Main problems. Practicing a few mixed-circuit numericals and concept-based MCQs with the above formulas gives you exam confidence.
For more step-by-step help on this and other physics concepts, Vedantu offers structured resources and detailed explanations aligned with the JEE syllabus—supporting your path to exam success.
FAQs on Inductive Reactance and Capacitive Reactance Explained
1. What is the formula for inductive reactance and capacitive reactance?
Inductive reactance is calculated using the formula XL = 2πfL, and capacitive reactance is given by XC = 1/(2πfC). These formulas help determine how inductors and capacitors oppose AC current.
- XL (Inductive Reactance): XL = 2πfL
- XC (Capacitive Reactance): XC = 1/(2πfC)
- Where f = frequency (Hz), L = inductance (H), C = capacitance (F)
2. What is the difference between inductive reactance and capacitive reactance?
Inductive reactance and capacitive reactance differ in how they oppose AC current and how they change with frequency.
- Inductive reactance (XL) increases with frequency, while capacitive reactance (XC) decreases as frequency increases.
- XL is due to inductors resisting changes in current; XC is due to capacitors opposing voltage change.
- Formula: XL = 2πfL; XC = 1/(2πfC)
- Phase difference: XL causes current to lag voltage; XC causes current to lead voltage.
3. What are the units and dimensional formulas of inductive and capacitive reactance?
Both inductive reactance (XL) and capacitive reactance (XC) are measured in ohms (Ω), and their dimensional formula is ML2T-3A-2.
- SI Unit: Ohm (Ω)
- Dimensional Formula: [ML2T-3A-2]
4. What is an example of inductive reactance in real life?
Inductive reactance is observed in devices like transformers, AC motors, and fluorescent tube ballasts, where inductors control the current flow in AC circuits.
- Used in electric fans and motors to limit sudden changes in current
- Transformers use inductive reactance to transfer energy between coils
5. How do you calculate the total reactance in a circuit?
The total reactance (X) in a series AC circuit is calculated by subtracting capacitive reactance from inductive reactance: X = XL - XC.
- If XL > XC, circuit behaves inductively
- If XC > XL, circuit behaves capacitively
- Total impedance (Z) is found using: Z = √[R² + (XL – XC)²]
6. What happens when inductive reactance and capacitive reactance are equal?
When inductive reactance (XL) equals capacitive reactance (XC), the circuit is said to be in resonance, and the effects of reactance cancel each other out.
- Net reactance (X) = 0
- Circuit impedance is minimum and equals resistance (R)
- Current is maximum in the circuit
7. What is the difference between reactance and resistance?
Resistance opposes both AC and DC current, dissipating energy as heat, while reactance only opposes AC current and does not dissipate energy.
- Resistance (R): Present in all circuits; remains constant for all frequencies
- Reactance (XL/XC): Depends on frequency; only in AC circuits (due to inductors and capacitors)
8. What factors affect inductive and capacitive reactance?
The main factors affecting inductive reactance (XL) and capacitive reactance (XC) are frequency of AC, inductance (L), and capacitance (C).
- XL increases with higher frequency and larger inductance (XL = 2πfL)
- XC decreases with increasing frequency and increases with smaller capacitance (XC = 1/(2πfC))
9. How do inductors and capacitors behave in DC circuits compared to AC circuits?
In DC circuits, an inductor acts as a short circuit after steady state is reached, and a capacitor behaves as an open circuit, so reactance is irrelevant.
- Inductors initially oppose change but have zero resistance to DC after steady current flows
- Capacitors block DC current once fully charged
- Reactance matters only in AC circuits
10. Why do inductive and capacitive reactances have opposite effects on phase?
Inductive reactance causes current to lag behind voltage, while capacitive reactance causes current to lead voltage, because of their different ways of storing and releasing energy.
- Inductor (XL): Current lags voltage by 90°
- Capacitor (XC): Current leads voltage by 90°
- These phase relationships are important in AC circuit analysis and resonance
11. What is the frequency dependence of inductive and capacitive reactance?
Inductive reactance (XL) increases directly with frequency, while capacitive reactance (XC) decreases with increasing frequency.
- XL = 2πfL: As frequency (f) increases, XL increases
- XC = 1/(2πfC): As frequency increases, XC decreases
