Difference Between Reactance and Impedance in Physics
Reactance and impedance are important concepts in the study of alternating current (AC) circuits. These terms describe the opposition that certain circuit elements provide to the flow of AC, similar to how resistance opposes the flow of direct current (DC).
In AC circuits, not only resistors but also capacitors and inductors contribute to this opposition. The unique properties of capacitors and inductors introduce two types of reactance—inductive and capacitive. The total effect of resistance and reactance combined is called impedance. Understanding how these quantities interact helps explain current and voltage behavior in real AC systems.
Reactance in AC Circuits
Reactance (symbol X) is the opposition to AC current provided by inductors and capacitors, separate from resistance.
Inductive reactance happens when an inductor is used. As AC voltage changes, the inductor resists changes in current by storing energy in its magnetic field. According to Faraday's and Lenz's laws, a changing magnetic field produces a voltage (emf) that opposes this change.
The formula for inductive reactance is:
- XL = Inductive reactance (Ohm, Ω)
- f = Frequency of the AC supply (Hertz, Hz)
- L = Inductance of the inductor (Henry, H)
Capacitive reactance is caused by capacitors, which resist changes in voltage by storing and releasing energy in their electric field. As a capacitor charges, its electric field opposes the applied voltage.
The formula for capacitive reactance is:
- XC = Capacitive reactance (Ohm, Ω)
- f = Frequency of the AC supply (Hz)
- C = Capacitance (Farad, F)
Impedance: Total Opposition in AC Circuits
Impedance (symbol Z) represents the total opposition to current in an AC circuit. It combines both resistance (R) and reactance (X). Impedance is always measured in Ohms (Ω).
The mathematical formula for impedance in a series RLC (resistor, inductor, capacitor) circuit is:
- Z = Impedance (Ω)
- R = Resistance (Ω)
- XL = Inductive reactance (Ω)
- XC = Capacitive reactance (Ω)
Key Formulas for Quick Revision
| Type | Formula | Unit | Meaning |
|---|---|---|---|
| Inductive Reactance | XL = 2πfL | Ohm (Ω) | Opposition by inductors |
| Capacitive Reactance | XC = 1/(2πfC) | Ohm (Ω) | Opposition by capacitors |
| Impedance (series RLC) | Z = √[R² + (XL - XC)²] | Ohm (Ω) | Total opposition in AC circuit |
Step-by-Step Problem-Solving Approach
- Identify known values for resistance (R), inductance (L), capacitance (C), and AC frequency (f).
- Calculate the inductive reactance using XL = 2πfL.
- Calculate the capacitive reactance using XC = 1/(2πfC).
- Find the net reactance (XL – XC).
- Use the impedance formula Z = √[R² + (XL – XC)²] to determine the total circuit opposition.
Worked Example
Suppose an AC circuit has a resistor of 10 Ω, an inductor of 0.05 H, and a capacitor of 100 μF connected in series. If the supply frequency is 50 Hz, what is the total impedance?
Let’s calculate step by step:
- Given: R = 10 Ω, L = 0.05 H, C = 100 μF = 100 x 10-6 F, f = 50 Hz
- Inductive reactance: XL = 2πfL = 2 x 3.14 x 50 x 0.05 ≈ 15.7 Ω
- Capacitive reactance: XC = 1 / (2πfC) = 1 / [2 x 3.14 x 50 x 100 x 10-6] ≈ 31.8 Ω
- Net reactance: XL – XC = 15.7 – 31.8 = -16.1 Ω
- Impedance: Z = √[10² + (-16.1)²] = √[100 + 259.21] ≈ 18.95 Ω
So, the total impedance for this circuit is approximately 18.95 Ω.
Table: Difference Between Reactance and Impedance
| Parameter | Reactance | Impedance |
|---|---|---|
| Nature | Opposition by inductors or capacitors | Combined opposition by resistance and reactance |
| Types | Inductive (XL) or Capacitive (XC) | Single value, combines R and X |
| Symbol | X | Z |
| Unit (SI) | Ohm (Ω) | Ohm (Ω) |
| Formula | XL = 2πfL, XC = 1/(2πfC) |
Z = √[R² + (XL – XC)²] |
| Where Present? | When only inductor or capacitor is in circuit | When resistance, inductor, and/or capacitor are in circuit |
Importance of Reactance and Impedance
Reactance and inductance make current in an AC circuit grow or decrease gradually, instead of changing instantly.
This property is useful in surge protection to prevent sudden changes in current that could damage electronic devices.
It also explains how circuits can selectively block or allow AC signals of different frequencies, a principle used in filters and tuning circuits.
Continue Learning and Practice
- For more on LCR circuits, see: LCR Circuit
- To understand series RLC analysis: AC Voltage Applied to Series LCR Circuit
- To learn about electrical impedance broadly: Electrical Impedance
- For phasor representation and more examples: Phasor Representation in AC
Practice more questions and review explanations on Vedantu’s Physics modules for mastery in circuits, reactance, and impedance topics.
FAQs on Reactance and Impedance in AC Circuits: Complete Guide
1. What is the difference between reactance and impedance?
Reactance is the opposition to the flow of alternating current (AC) due to capacitors and inductors, while impedance is the total opposition faced by AC, combining resistance and reactance.
- Reactance (X): Caused by inductors (XL) and capacitors (XC)
- Impedance (Z): Combines resistance (R) and net reactance, calculated as Z = √(R² + (XL − XC)²)
2. What is reactance in an AC circuit?
Reactance is the opposition offered by inductors and capacitors to the flow of AC.
- There are two types: Inductive Reactance (XL) and Capacitive Reactance (XC).
- It depends on frequency and is measured in ohms (Ω).
3. How do you calculate inductive reactance (XL) and capacitive reactance (XC)?
Use these key formulas to calculate reactance:
- Inductive Reactance: XL = 2πfL
- Capacitive Reactance: XC = 1/(2πfC)
4. What is the formula for total impedance in a series LCR circuit?
The total impedance Z in a series LCR (resistor, inductor, capacitor) circuit is given by:
Z = √(R² + (XL − XC)²)
Here, R is resistance (Ω), XL is inductive reactance, and XC is capacitive reactance.
5. What is the SI unit of reactance and impedance?
Both reactance (X) and impedance (Z) have the SI unit of ohm (Ω).
- This aligns their measurement with resistance (R).
6. How are resistance, reactance, and impedance different?
Resistance (R): Opposition due to resistors, constant for both AC and DC.
Reactance (X): Opposition due to inductors/capacitors, only in AC and frequency-dependent.
Impedance (Z): Combined effect of resistance and reactance. It represents the total opposition in an AC circuit: Z = √(R² + (XL − XC)²).
7. What is the physical meaning of reactance?
Reactance represents how inductors and capacitors oppose changes in current in an AC circuit without dissipating energy as heat.
- Inductive Reactance (XL): Due to energy stored in magnetic fields.
- Capacitive Reactance (XC): Due to energy stored in electric fields.
8. How do you measure impedance in an AC circuit?
Impedance can be measured using an AC source:
- Apply a known AC voltage (V) to the circuit.
- Measure the resulting current (I).
- Calculate impedance as Z = V/I at that frequency.
9. Why is impedance important in AC circuits?
Impedance determines how much current flows in an AC circuit and affects power transfer, voltage drops, and phase difference between current and voltage.
- Essential for designing and analyzing LCR and other AC circuits.
- Affects resonance and filter behavior in electronics.
10. What are XL and XC in AC circuits?
XL stands for Inductive Reactance and opposes changes in current due to inductors.
XC stands for Capacitive Reactance and opposes changes in voltage due to capacitors.
- Both affect AC current flow but in opposite ways: XL increases with frequency, XC decreases with frequency.
11. How does frequency affect reactance and impedance?
Frequency has opposite effects on inductive and capacitive reactance:
- Inductive Reactance (XL): Increases with frequency (XL ∝ f).
- Capacitive Reactance (XC): Decreases with frequency (XC ∝ 1/f).
- Impedance (Z): Changes depending on the net values of XL and XC at a given frequency.
12. Can you give an example problem involving reactance and impedance?
Example:
An AC circuit has a 10 Ω resistor, 0.05 H inductor, and 100 μF capacitor in series at 50 Hz.
- XL = 2π × 50 × 0.05 = 15.7 Ω
- XC = 1/(2π × 50 × 100 × 10⁻⁶) ≈ 31.8 Ω
- Net Reactance = XL − XC = 15.7 − 31.8 = -16.1 Ω
- Z = √(10² + (-16.1)²) ≈ 18.95 Ω
