SATHEE: Shortcut Methods

Shortcut Methods

Shortcut Methods and Tricks for LC Oscillations

JEE Mains

1. Resonance Formula

$f_{0} = \frac{1}{2 π \sqrt{L C}}$

Where:

$f_{0}$ is the resonant frequency in Hz
$L$ is the inductance in Henry
$C$ is the capacitance in Farads

2. Time Period Formula

$T_{0} = \frac{2 π \sqrt{L C}}{1}$

Where:

$T_{0}$ is the time period in seconds
$L$ is the inductance in Henry
$C$ is the capacitance in Farads

3. Energy Storage Formula

The total energy stored in an LC circuit at any instant is given by:

$E = \frac{1}{2} L I^{2} + \frac{1}{2} C V^{2}$

Where:

$E$ is the total energy stored in Joules
$L$ is the inductance in Henry
$I$ is the current in Amperes
$C$ is the capacitance in Farads
$V$ is the voltage in Volts

4. Quality Factor (Q) Formula

The quality factor (Q) of an LC circuit is a measure of its efficiency. It is given by:

$Q = \frac{ω L}{R}$

Where:

$Q$ is the quality factor
$ω$ is the angular frequency
$L$ is the inductance in Henries
$R$ is the resistance in Ohms

CBSE Boards

1. Resonance Formula

$f_{0} = \frac{1}{2 π \sqrt{L C}}$

Where:

$f_{0}$ is the resonant frequency in Hertz
$L$ is the inductance in Henry
$C$ is the capacitance in Farads

2. Time Period Formula

$T_{0} = \frac{1}{f_{0}}$

Where:

$T_{0}$ is the time period in seconds
$f_{0}$ is the resonant frequency in Hertz

3. Energy Storage Formula

$E = \frac{1}{2} C V^{2}$

Where:

$E$ is the energy stored in Joules
$C$ is the capacitance in Farads
$V$ is the voltage across the capacitor in Volts

4. Quality Factor (Q) Formula

$Q = \frac{1}{R} \sqrt{\frac{L}{C}}$

Where:

$Q$ is the quality factor
$R$ is the resistance of the inductor in ohms
$L$ is the inductance of the inductor in Henries
$C$ is the capacitance of the capacitor in Farads

Shortcut Methods

Shortcut Methods and Tricks for LC Oscillations

JEE Mains

CBSE Boards

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

Shortcut Methods

Shortcut Methods and Tricks for LC Oscillations

JEE Mains

CBSE Boards

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

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