Reactance — Revision Notes

⚡ 30-Second Revision

Inductive Reactance ($X_L$): — Opposition by inductor to AC. $X_L = \omega L = 2\pi f L$. Directly proportional to $f$. Voltage leads current by $90^\circ$. At DC ($f=0$), $X_L=0$ (short circuit).
Capacitive Reactance ($X_C$): — Opposition by capacitor to AC. $X_C = 1/(\omega C) = 1/(2\pi f C)$. Inversely proportional to $f$. Current leads voltage by $90^\circ$. At DC ($f=0$), $X_C=\infty$ (open circuit).
Units: — Both $X_L$ and $X_C$ are measured in Ohms (\Omega).
Difference from Resistance: — Reactance stores/returns energy; resistance dissipates energy. Reactance causes phase shift; resistance doesn't.

2-Minute Revision

Reactance is the opposition offered by inductors and capacitors to alternating current (AC), distinct from resistance. Inductive reactance ($X_L$) arises from an inductor's opposition to current changes, given by $X_L = 2\pi f L$.

It's directly proportional to frequency ($f$) and inductance ($L$). In a pure inductor, voltage leads current by $90^\circ$. At DC ($f=0$), an inductor acts as a short circuit. Capacitive reactance ($X_C$) stems from a capacitor's opposition to voltage changes, given by $X_C = 1/(2\pi f C)$.

It's inversely proportional to frequency ($f$) and capacitance ($C$). In a pure capacitor, current leads voltage by $90^\circ$. At DC ($f=0$), a capacitor acts as an open circuit. Both reactances are measured in ohms.

Key for NEET is understanding these formulas, their frequency dependence, and the phase relationships, as they form the basis for impedance and resonance in AC circuits.

5-Minute Revision

Reactance is the dynamic opposition to AC current flow offered by energy-storing components: inductors and capacitors. It's crucial to distinguish it from resistance, which dissipates energy. Reactance, measured in ohms, stores energy in magnetic or electric fields and returns it to the circuit, resulting in a $90^\circ$ phase difference between voltage and current.

**Inductive Reactance ($X_L$):** An inductor's opposition to AC is $X_L = \omega L = 2\pi f L$. This means $X_L$ increases linearly with frequency ($f$) and inductance ($L$). At low frequencies, $X_L$ is small, making the inductor behave almost like a short circuit.

At high frequencies, $X_L$ is large, making it behave like an open circuit. In a purely inductive circuit, the voltage across the inductor leads the current through it by $90^\circ$. For example, a $0.

5, ext{H}$inductor at$100, ext{Hz}$has$X_L = 2\pi \times 100 \times 0.5 = 100\pi \approx 314,Omega$.

**Capacitive Reactance ($X_C$):** A capacitor's opposition to AC is $X_C = 1/(\omega C) = 1/(2\pi f C)$. This shows $X_C$ is inversely proportional to frequency ($f$) and capacitance ($C$). At low frequencies, $X_C$ is very large, making the capacitor behave like an open circuit.

At high frequencies, $X_C$ is small, making it behave like a short circuit. In a purely capacitive circuit, the current through the capacitor leads the voltage across it by $90^\circ$. For example, a $10,mu\text{F}$ capacitor at $100,\text{Hz}$ has $X_C = 1/(2\pi \times 100 \times 10 \times 10^{-6}) = 1/(2\pi \times 10^{-3}) = 1000/(2\pi) \approx 159,Omega$.

NEET Focus: Remember the formulas, their frequency dependence, and the phase relationships. Be prepared for questions that involve calculating $X_L$ or $X_C$, comparing their values at different frequencies, or identifying the phase lead/lag. Also, understand their behavior at DC ($f=0$) – inductor as short, capacitor as open. These concepts are foundational for understanding impedance and resonance in RLC circuits.

Prelims Revision Notes

Reactance: Key Facts for NEET UG

1. Definition: Reactance is the opposition offered by inductors and capacitors to the flow of alternating current (AC). It's measured in Ohms (\Omega).

2. Types of Reactance:

* **Inductive Reactance ($X_L$):** * Caused by inductors (coils). * Formula: $X_L = \omega L = 2\pi f L$. * Frequency Dependence: $X_L \propto f$ (directly proportional). As frequency increases, $X_L$ increases.

* Phase Relationship: Voltage leads current by $90^\circ$ (or $\pi/2$ radians). Mnemonic: ELI (Voltage E leads Current I in Inductor L). * **DC Behavior ($f=0$):** $X_L = 0$. An ideal inductor acts as a short circuit for DC.

* **Capacitive Reactance ($X_C$):** * Caused by capacitors. * Formula: $X_C = 1/(\omega C) = 1/(2\pi f C)$. * Frequency Dependence: $X_C \propto 1/f$ (inversely proportional). As frequency increases, $X_C$ decreases.

* Phase Relationship: Current leads voltage by $90^\circ$ (or $\pi/2$ radians). Mnemonic: ICE (Current I leads Voltage E in Capacitor C). * **DC Behavior ($f=0$):** $X_C \to \infty$. An ideal capacitor acts as an open circuit for DC (after charging).

3. Key Distinctions from Resistance:

* Energy: Reactance stores and returns energy; resistance dissipates energy as heat. * Phase: Reactance causes a $90^\circ$ phase shift; resistance causes $0^\circ$ phase shift. * Frequency: Reactance is frequency-dependent; ideal resistance is not.

4. Important Formulas to Memorize:

* $X_L = 2\pi f L$ * $X_C = 1/(2\pi f C)$ * $\omega = 2\pi f$

5. Common Traps & Tips:

* Unit Conversion: Always convert mH to H ($1,\text{mH} = 10^{-3},\text{H}$) and \mu F to F ($1,mu\text{F} = 10^{-6},\text{F}$). Errors here are common. * Frequency Dependence: Don't mix up the direct and inverse proportionality.

Visualize the graphs of $X_L$ vs $f$ (straight line through origin) and $X_C$ vs $f$ (hyperbola). * Phase: Clearly remember ELI and ICE. This is a frequent conceptual question. * Resonance: At resonance, $X_L = X_C$.

This leads to the resonant frequency formula $f_0 = 1/(2\pi \sqrt{LC})$. Be ready to derive or apply this.

6. Practice: Solve numerical problems involving direct calculation, frequency changes, and comparison of $X_L$ and $X_C$. Understand how reactance contributes to overall impedance in RLC circuits.

Vyyuha Quick Recall

ELI the ICE man

ELI: — In an E (voltage) leads L (inductor) I (current) circuit, voltage leads current.
ICE: — In an I (current) leads C (capacitor) E (voltage) circuit, current leads voltage.

This helps remember the $90^\circ$ phase relationships for ideal inductors and capacitors.