The Series RLC Circuit: Group Worksheet Intro Part 1: Resistive Loads Describe how an increase in resistance will affect the peak current in AC circuit with only a generator and resistor. Describe how an increase in frequency will affect the peak current and phase difference between current and voltage. Intro Part 2: Alternating Current in a Capacitor Construct a v vs. t and i vs. t graph (on the same set of axis) for a simple RC series circuit paying special attention to any phase differences between the voltage and current. Suppose that the capacitance is increased, how does this affect the peak current and the phase difference between the current and voltage? Now supposed the frequency is increased, with capacitance unchanged. Describe how this would affect the peak current and phase difference between the current and voltage. Intro Part 3: Alternating Current in an Inductor For a purely inductive circuit, what does the vL(t) and IL(t) vs t graph look like? Sketch them below. Suppose that the inductance is increased, how does this affect the peak current and the phase difference between the current and voltage? As the frequency is increased in the circuit, what happens? How does this affect the phase difference and peak current? RLC Simulation Predict the resonant frequency of a circuit with R=5Ω, C=250µF, and L=50mH by using equation (11). Show your calculation. Find the resonant frequency by changing the top slider for the AC generator and watching for the maximum current. Agree? Yes / No (if no – why??) If inductance is increased by a small amount, with the resistance and capacitance unchanged, how does this affect the peak current and phase angle between the current and the voltage? How does this affect the resonant frequency and why? If capacitance is increased by a small amount, with the resistance and inductance unchanged, how does this affect the peak current and phase angle between the current and the voltage? How does this affect the resonant frequency and why? Take Data! For varying ω, measure IR to calculate VR. Ω IR VR Plot VR/VR Max vs. frequency, where VR Max is the maximum value of VR. Sketch below. What does the shape of this graphic indicate? How is that information useful? What factors would change the overall shape of this curve? Pick an ω that is below ω0 where I is appreciably smaller than at resonance, calculate VR using I=VR/R. Calculate the reactance of both the inductor and the capacitor using the calculated current equations (3) and (5). Calculate the phase angle from equation (8). Show calculations. Using the supporting simulation, recreate your parameters for the circuit with this simulation. How do your predictions compare to the phasor diagram in the simulation? Pick an ω that is above ω0 where I is appreciably smaller than at resonance, calculate VR using I=VR/R. Calculate the reactance of both the inductor and the capacitor using the calculated current equations (3) and (5). Calculate the phase angle from equation (8). Show calculations. Compare the phase angle to phasor diagram simulation. Set up some other values for the components in the circuit and see how these values affect both the resonance frequencies, the phase shift, and the phasor diagrams. What situations would you design a circuit with a large capacitor? A small capacitor? A large inductor? A small inductor?

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