Physics Chapter 10: DC Circuits

Chapter 10: DC Circuits

• Ohm's Law: States the relationship between voltage (V), current (I), and resistance (R) in a circuit. Mathematically expressed as V = IR.
• Resistance: Opposition to current flow. Measured in ohms (Ω).
• Factors Affecting Resistance:
• Resistivity (ρ): Resistance depends on the material's resistivity (ρ). Formula: R = ρL/A, where L is length and A is cross-sectional area.
• Length (L): Longer conductors have higher resistance.
• Cross-sectional Area (A): Wider conductors have lower resistance.
• Temperature (T): Resistance generally increases with temperature. Formula for temperature dependence: R = R₀(1 + αΔT), where R₀ is initial resistance, α is the temperature coefficient of resistance, and ΔT is the change in temperature.
• Power Dissipation: Power (P) dissipated in a resistor is given by P = IV = I²R = V²/R.
• Maximum Power Transfer: Occurs when the load resistance equals the internal resistance of the source. (Diagram required for visual representation)
• Kirchhoff's Current Law (KCL): The sum of currents entering a junction equals the sum of currents leaving the junction.
• Kirchhoff's Voltage Law (KVL): The algebraic sum of all voltages around any closed loop in a circuit is zero.
• Resistors in Series: The equivalent resistance of resistors connected in series is the sum of their individual resistances (R_eq = R₁ + R₂ + ...).
• Resistors in Parallel: The reciprocal of the equivalent resistance of parallel resistors is the sum of the reciprocals of their individual resistances (1/R_eq = 1/R₁ + 1/R₂ + ...).

Chapter 11: Simple Harmonic Motion (SHM)

• Simple Harmonic Motion (SHM): A periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and is directed towards it.
• Conditions for SHM:
• Restoring force must be proportional to displacement.
• Restoring force must be directed towards the equilibrium position.
• SHM under Elastic Restoring Force: Examples include a mass on a spring, exhibiting oscillations.
• Motion of Projection of Circular Motion: The projection of a particle moving in a uniform circular motion onto a diameter exhibits simple harmonic motion.
• Instantaneous Velocity: Instantaneous velocity in SHM can be derived as a function of displacement (v = ±ω√(A² - x²)).
• Simple Pendulum: A simple pendulum, under small oscillations, approximates SHM.
• Free and Forced Oscillations: Free oscillations occur without external forces; forced oscillations are driven by an external periodic force.
• Forced Oscillations and Resonance: Resonance occurs when the driving frequency matches the natural frequency of the system, leading to maximum amplitude of oscillations.