Voltage and Current in RLC Circuits ?If circuit contains only R + emf source current is simple. ?If L and/or C present
When a voltage source is connected to an RLC circuit energy is provided to compensate resistance to current flow increases with frequency.
The objective of this work is an attempt to minimize these errors through application of an approximation algorithm that allows to determine parameters of
(characteristic) equation of s determined by the circuit parameters: Example 8.2: Discharging a parallel RLC circuit (1).
accuracy of the DTM for solving the linear and nonlinear higher order differential equations and. RLC circuit problems some illustrative example are.
Example 9.3. The circuit below reduces to a simple parallel RLC circuit after t = 0. Determine an expression for the resistor current i.
Given the power factor and values of X and R in an ac circuit compute the value of Figure 4-4 is the schematic diagram of the series RLC circuit.
Determine the real reactive
3. Determine the response type by calculating wo and a. For both series and parallel RLC circuits. LC. The computation of a depends on the configuration of
consider second-order RLC circuits from two distinct perspectives: Step Response of RLC Circuit. ? Determine the response of the following RLC circuit.
Power Example 1 (cont) ÎR = 200? X C = 150? X L = 80? ? rms = 120v f = 60 Hz ÎHow much capacitance must be added to maximize the power in the circuit (and thus bring it into resonance)? Want X C = X L to minimize Z so must decrease X C So we must add 15 5?F capacitance to maximize power XfCC C XX C CLnew new==? =80 33 2?F
Figure 2 shows the response of the series RLC circuit with L=47mH C=47nF and for three different values of R corresponding to the under damped critically damped and over damped case We will construct this circuit in the laboratory and examine its behavior in more detail (a) Under Damped R=500? (b) Critically Damped R=2000 ? (c) Over Damped
RLC Circuit Example ÎCircuit parameters L = 12mL C = 1 6?F R = 1 5? ÎCalculate ? ?’ f and T ?= 7220 rad/s ?’ = 7220 rad/s f = ?/2?= 1150 Hz T = 1/f = 0 00087 sec ÎTime for q max to fall to ½ its initial value t = (2L/R) * ln2 = 0 0111s = 11 1 ms # periods = 0 0111/ 00087 ?13 ?=×=1/ 0 012 1 6 10 7220()(?6)
Series/Parallel RLC circuits A general RLC circuit (with one inductor and one capacitor) also leads to a second-order ODE As an example consider the following circuit: i C L V0 V R2 R1 V0 = R1 i + L di dt + V (1) i = C dV dt + 1 R2 V (2) Substituting (2) in (1) we get V0 = R1 CV0+ V=R2 + L CV00+ V0=R2 + V ; (3) V00[LC] + V0[R1C + L=R2] + V
Summary of the properties of RLC resonant circuits Example: very useful circuit for rejecting noise at a certain frequency such as the interference due to 60 Hz line power is the band reject filter sown below Vs L C +VR - Figure 6 The impedance seen by the source is ? L = R+ (1 28) ?? LC ? = ?=When 0 an open circuit
circuit containing a resistor a capacitor and an inductor is called an RLC circuit (or LCR) asshown in Figure 1b With a resistor present the total electromagnetic energy is no longer constant sinceenergy is lost via Joule heating in the resistor The oscillations of charge current and potential are nowcontinuously decreasing with amplitude