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. cosϕ 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=10Ω, L=0.1H, and C=10μF connected to a 50 Hz supply, calculate the impedance. XL=2π×50×0.1=31.4ΩXC=2π×50×10×10−61=318.3ΩZ=102+(31.4−318.3)2≈287Ω
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, XL=XC, 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.