convention V0 is real) and assume that I(t) = I0eiωt where I0 is a general complex number (which can be written quite generally as I0 = |I0|e−iδ), and where one gets physical answers at the end by taking the real part of the complex answers. Find an algebraic complex expression that expresses the sum of the voltages. Solve this expression directly using algebra, no pictures of “phasors” really required. Factor out the solution to obtain |I0|, δ, Z (the complex impedance), and the voltages across each element
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).
Derive the full solution to the driven LRC circuit shown below using complex exponentials. Start with
Kirchhoff’s rule for the loop and assume a complex V (t) = V0eiωt (where by convention V0 is real) and
assume that I(t) = I0eiωt where I0 is a general complex number (which can be written quite generally
as I0 = |I0|e−iδ), and where one gets physical answers at the end by taking the real part of the
complex answers. Find an algebraic complex expression that expresses the sum of the voltages. Solve this expression directly using algebra, no pictures of “phasors” really required. Factor out the solution to obtain
|I0|, δ, Z (the complex impedance), and the voltages across each element as a function of time.
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