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RCL circuits Resistor, Capacitor and Inductor are in one simple circuit

RCL circuits Resistor, Capacitor and Inductor are in one simple circuit. Allow charge to get stored into the capacitor. When switch is flipped to B, charge begins to flow out of the capacitor, which increases the current

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RCL circuits Resistor, Capacitor and Inductor are in one simple circuit

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  1. RCL circuitsResistor, Capacitor and Inductor are in one simple circuit

  2. Allow charge to get stored into the capacitor • When switch is flipped to B, charge begins to flow out of the capacitor, which increases the current • Change in current results in change in flux; inductor fights this and current decreases • Current begins to increase as inductor fights it less • This results in charge to begin getting stored on capacitor again • Resulting decrease in current causes inductor to fight as it wants current to continue flowing • The inductor and capacitor will continue to go back and forth in harmonic oscillation type fashion

  3. But there’s a resistor. . . • The presence of the resistor will result in more energy being dissipated as heat • Thus it acts as a damper to the oscillations; current will eventually decrease for good

  4. Relevant Equations • ε = εosinωt • The emf is induced by the changing current; as discussed this will act as an oscillator • I = ε/R = Iosinωt • ω = f = • The resulting frequencies • Energy at any given time would be that stored in both the capacitor and inductor

  5. More Relevant Equations • Since the rate of energy dissipation through the resistor is I2·R, we have:

  6. Setting up a Diff Eq. . . Divide both sides by L  • In terms of the AP exam, they would probably only ask you to set this up, if that. They would not ask for the solution • The equation of motion for the damped harmonic oscillator is: • They’re both similar formats of each other

  7. A series RLC circuit has a peak current of 4 A with a frequency of 29 kHz. If the resistance of the circuit is 56 kohm, the capacitance of the circuit is 11 uF, and the inductance of the circuit is 26 H, determine the average power of the circuit over one cycle. • a. 1.3*10^6 W • b. 4.5*10^5 W • c. 1.3*10^5 W • d. 7.2*10^4 W power P = I^2 R P = 2.82^2 ( 56 x10^3) P =4.47 x 10^5 watts the answer is B .

  8. Find the emf of a circuit with an 2W inductor, 3F capacitor and a 20ohm resistor 30 seconds after closing the circuit

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