Q No. 2 (a): An RCL circuit (as shown in Figure) has C = 5.56 x 10-3 farad, L = 20 henries. After charging the capacitor, the switch is thrown to b (i.e. at t = 0). Find the resistance (R) of the resistor for critical damping (i.e. when the characteristic equation of the associated ODE has a single repeated root).
Q No. 2 (a): An RCL circuit (as shown in Figure) has C = 5.56 x 10-3 farad, L = 20 henries. After charging the capacitor, the switch is thrown to b (i.e. at t = 0). Find the resistance (R) of the resistor for critical damping (i.e. when the characteristic equation of the associated ODE has a single repeated root).
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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).
Question
Transcribed Image Text:Q No. 2 (a): An RCL circuit (as shown in Figure) has C = 5.56 x 103 farad, L = 20 henries. After
charging the capacitor, the switch is thrown to b (i.e. at t = 0). Find the resistance (R) of the
resistor for critical damping (i.e. when the characteristic equation of the associated ODE has
a single repeated root).
a
Q No. 2 (b): For the same RCL circuit of 2(a), find the normalized solutions of the
corresponding ODE. Determine equations for the subsequent charge (as a function of t) on
the capacitor and the current in the circuit. It is given that when the switch S was thrown to
b (i.e. at t = 0), the initial charge on capacitor was 1 Coulomb.
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