Electric Circuits

Current, Voltage, and Resistance

Electric circuits involve the flow of electric charge, described by current, voltage, and resistance. Understanding their relationships is fundamental to analyzing circuits.

• Current (I): The rate of flow of electric charge. Defined as , where is the charge and is the time interval.

• Ohm's Law: Relates voltage (V), current (I), and resistance (R):

• Resistance (R): Opposition to current, given by:

Where is resistivity, is length, and is cross-sectional area.

Power in Electric Circuits

• Power (P): The rate at which energy is used or dissipated in a circuit:

Resistors in Series and Parallel

• Series: Same current flows through all resistors; total resistance is the sum.

• Parallel: Same voltage across all resistors; total resistance is given by:

• Current in Series:

• Voltage in Series:

• Voltage in Parallel:

• Current in Parallel:

Oscillations and Simple Harmonic Motion

Spring Force and Newton's Second Law

• Hooke's Law (Spring Force): The restoring force of a spring is proportional to its displacement:

• Newton's Second Law: The net force on an object equals mass times acceleration:

Frequency, Period, and Angular Frequency

• Frequency (f): Number of oscillations per second.

• Period (T): Time for one complete oscillation:

• Angular Frequency (\omega):

Energy in Simple Harmonic Motion

• Total Mechanical Energy: The sum of kinetic and potential energy in a mass-spring system:

• Velocity as a Function of Position:

Equations of Motion for a Mass on a Spring

• Period:

• Angular Frequency:

• Displacement: or

• Velocity: or

• Acceleration: or

Waves and Sound

Wave Speed and Linear Density

• Linear Density (\mu): Mass per unit length of a string:

• Wave Speed on a String:

• Wave Speed in a Medium: For sound in a solid or fluid:

Where is the bulk modulus and is the density.

Wave Properties

• Relationship between Speed, Wavelength, and Frequency:

Intensity and Sound Level

• Intensity (I): Power per unit area:

For a spherical source,

• Inverse Square Law for Intensity:

• Reference Intensity ():

• Sound Level (\beta) in Decibels (dB):

• Intensity from Sound Level:

Heat Capacities of Gases (Adiabatic Index)

• Adiabatic Index (\gamma): Ratio of heat capacities for different types of gases:

Additional info: The adiabatic index is important in thermodynamics and the study of sound propagation in gases.

Summary Table: Key Equations