LCR Circuit-Graphical Solution-Alternating Currents

Phase difference and impedance

• Phase difference: The phase difference between voltage and current in an AC circuit is the angle by which the current lags or leads the voltage.
• Impedance: The impedance of an AC circuit is the effective resistance to the flow of current. It is calculated as the square root of the sum of the squares of the resistance, inductive reactance, and capacitive reactance.

Phasor diagrams

• Phasor diagrams are graphical representations of the voltage and current phasors in an AC circuit.
• Phasor diagrams help in visualising the phase relationships and calculating the circuit parameters.

Resonance

• Resonance is the phenomenon of maximum current flow in an AC circuit when the circuit’s impedance is minimum.
• The resonant frequency is the frequency at which resonance occurs.

Power in an AC circuit

• Average power is the power that is dissipated in the circuit over one complete cycle.
• Reactive power is the power that is stored in the circuit’s magnetic field and electric field.
• Power factor is the ratio of average power to apparent power.

Quality factor (Q-factor)

• Q-factor is a measure of the circuit’s ability to store energy and release it over time.
• A high Q-factor indicates a higher energy storage capacity.

RLC circuit analysis

• RLC circuits are circuits that consist of a combination of resistors, inductors, and capacitors.
• The transient response of an RLC circuit is the behaviour of the circuit immediately after it is switched on.
• The steady-state response of an RLC circuit is the behaviour of the circuit after it has reached a constant state.

Applications of LCR circuits

• LCR circuits are used in a variety of electrical and electronic devices, including filters, oscillators, and resonant circuits.
• Filters are used to remove unwanted frequencies from a signal.
• Oscillators are used to generate AC signals.
• Resonant circuits are used to select a specific frequency from a signal.

Reference to NCERT books for 11th and 12th classes

• NCERT Physics Part 1 (Class 11): Chapter 7 - Alternating Current
• NCERT Physics Part 2 (Class 12): Chapter 7 - Alternating Current