LR Circuit Equation Derivations (10:05)
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Today, we're diving deep into LR circuits, deriving equations for current and its time rate of change. Closing the switch at t equals zero, we employ Kirchhoff’s Loop Rule, employing u-substitution for a smoother journey. Through meticulous steps, we integrate and identify limits, ensuring a comprehensive understanding. Billy clarifies time limits, guiding us through the math, leading to the ultimate expression for current: emf over resistance times (1 - e^(-Rt/L)). This aligns perfectly with circuit limits, from zero at t equals zero to emf over resistance in the steady state. Bo then skillfully tackles the time rate of change of current, yielding emf over inductance times e^(-Rt/L). Witness the elegance of physics unfolding before us! 🌌✨
Chapters: 0:00 Introduction 0:49 Deriving Current as a Function of Time 7:50 Deriving Time Rate of Change of Current as a Function of Time
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