The resistance, inductance, and capacitance in a parallel RLC circuitare 1 kΩ, 12.5 H, and 2 μF, respectively.1. Calculate the roots of the characteristic equation that describe thevoltage response of the circuit.2. Will the response be over-, under-, or critically damped?3. What value of R will yield a damped frequency of 120 rad/s?4. What are the roots of the characteristic equation for the value of Rfound in (c)?5. What value of R will result in a critically damped response?
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 resistance, inductance, and capacitance in a parallel RLC circuit
are 1 kΩ, 12.5 H, and 2 μF, respectively.
1. Calculate the roots of the characteristic equation that describe the
voltage response of the circuit.
2. Will the response be over-, under-, or critically damped?
3. What value of R will yield a damped frequency of 120 rad/s?
4. What are the roots of the characteristic equation for the value of R
found in (c)?
5. What value of R will result in a critically damped response?
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