Alternating Current - Comprehensive NEET Physics Notes

1. Key Formulae Extraction:

• Ohm’s Law for AC Circuits: $V_m=I_{m}R$
• RMS Values: $I_{rms}=\frac{I_m}{\sqrt{2}}\approx 0.707I_m$ $V_{rms}=\frac{V_m}{\sqrt{2}}\approx 0.707V_m$
• Power in AC Circuit: $P_{avg}=V_{rms}\cdot I_{rms}\cdot \cos \varphi$
• Inductive Reactance: $X_L=\omega L$
• Capacitive Reactance: $X_C=\frac{1}{\omega C}$
• Impedance in an LCR Circuit: $Z=\sqrt{R^2+(X_L-X_C{)}^2}$
• Resonant Frequency: ${\omega }_0=\frac{1}{\sqrt{LC}}$

2. Formula Explanation:

• Ohm’s Law for AC Circuits: This relates the peak voltage and current in a purely resistive circuit. It is analogous to the Ohm's law used in DC circuits.
• RMS Values: The RMS (Root Mean Square) values are used because they represent the equivalent DC values that would produce the same heating effect in a resistor.
• Power in AC Circuits: The average power consumed in an AC circuit depends on the phase difference between the voltage and current. $\cos \varphi$ is known as the power factor.
• Inductive and Capacitive Reactance: These quantify the opposition to the current in inductors and capacitors respectively. The inductive reactance increases with frequency, while the capacitive reactance decreases.
• Impedance in an LCR Circuit: Impedance is the total opposition to current in the circuit, combining resistive, inductive, and capacitive effects.
• Resonant Frequency: At this frequency, the inductive and capacitive reactances cancel each other, and the circuit behaves as a purely resistive circuit with minimum impedance.

3. Derivations:

• Derivation of RMS Values: Starting from the sinusoidal expressions for current and voltage, the RMS values are derived by taking the square root of the mean of the squares of the instantaneous values over a complete cycle.
• Derivation of Impedance in LCR Circuit: Using Kirchhoff’s Voltage Law (KVL), the impedance is derived by considering the vector sum of resistive, inductive, and capacitive voltage drops.

4. Example Applications:

• Example Problem (Impedance Calculation): Given an LCR circuit with $R=10\Omega$, $L=0.1H$, and $C=10\mu F$ connected to a 50 Hz supply, calculate the impedance. $X_L=2\pi \times 50\times 0.1=31.4\Omega$ $X_C=\frac{1}{2\pi \times 50\times 10\times 10^{-6}}=318.3\Omega$ $Z=\sqrt{10^2+(31.4-318.3{)}^2}\approx 287\Omega$

5. Common Mistakes:

• Confusing Peak and RMS Values: Always check whether the question asks for peak or RMS values.
• Incorrect Phase Angle Calculation: Be mindful of whether the current leads or lags the voltage, especially in capacitive or inductive circuits.
• Forgetting Resonance Conditions: At resonance, $X_L=X_C$, leading to minimum impedance. Neglecting this can lead to incorrect impedance calculations.

6. Final Review and Formatting:

• Organization: Ensure the formulae are grouped logically, starting with basic concepts and progressing to more complex ones.
• Clarity: Use clear headings and subheadings for each section, and keep explanations concise.
• Quick Revision: Include a summary table of all the key formulae at the end for quick reference.

This format should be clear and helpful for students preparing for the NEET UG Physics exam.