A simple electrical circuit consists of a resistor with a resistance R = 10, an inductor with an inductance L = 1 H, a DC power source with a voltage V = 10 volts and a switch S all in series. If the switch S is closed a time t = 0, then from kirchhoff's law the current is governed by the following differential equation. dl L-+RI = V dt (a) Using the integrating factor, solve the differential equation to find I as a function of time t. (b) Find the Laplace Transform I(s) of the current I by applying the Laplace transform to the two sides of the differential equation at zero initial conditions, that is I(0) = 0. (c) Solve the differential equation by finding I from its Laplace transform I(s). 5.

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Sinusoids And Phasors

Sinusoids are defined as the mathematical waveforms that are used to describe the nature of periodic oscillations.

Circuit Theory

Electric circuits are a network that comprises of a closed-loop, which helps in providing a return path for the current through a switch. When the switch is activated, the load operates, and the current accepts a path to finish the circuit at a low potential level from the opposing high potential level. Electric circuits theory is a linear analysis that helps in establishing a linear relation of voltage and current for R (resistance), L (inductance), and C (capacitance).