Consider an LRC series circuit with a resistance of 2.5 ohms, capacitance of 0.1 farad, an inductance of 0.1 henry and electromotive force, volts. Given that Assume there is no initial charge and no initial current on the capacitor. a) Find the equation of the charge q(t), on the capacitor at any time t. (Do not solve the coefficients). b) Name two methods that can be used to find the particular solution qp(t). c) Write your assumption to solve for the particular solution based on each method answered in (b).
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).
Consider an LRC series circuit with a resistance of 2.5 ohms, capacitance of 0.1 farad, an
inductance of 0.1 henry and electromotive force, volts. Given that
Assume there is no initial charge and no initial current on the
capacitor.
a) Find the equation of the charge q(t), on the capacitor at any time t.
(Do not solve the coefficients).
b) Name two methods that can be used to find the particular solution qp(t).
c) Write your assumption to solve for the particular solution based on each method
answered in (b).
d) State the equation of the current, i(t).
e) State the transient and the steady-state current.
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