iR ic R c Vo Figure 8.1 Full Alternative Text
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).
The initial value of the voltage v in the circuit is zero,
and the initial value of the capacitor current, ic(0+), is 45 mA. The
expression for the capacitor current is known to be
ic(t)=A1e−200t+A2e−800t, t≥0+,
when R is 250 Ω. Find
1. the values of α, ω0, L, C, A1, and A2
(Hint:diC(0+)dt=−diL(0+)dt−diR(0+)dt=−v(0)L−1RiC(0+)C)
1. the expression for v(t), t≥0,
2. the expression for iR(t)≥0,
3. the expression for iL(t)≥0
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