Learning Goal: To understand the use of phasor diagrams in calculating the impedance and resonance conditions in a serie

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Learning Goal To Understand The Use Of Phasor Diagrams In Calculating The Impedance And Resonance Conditions In A Serie 1 (118.32 KiB) Viewed 40 times

Learning Goal: To understand the use of phasor diagrams in calculating the impedance and resonance conditions in a series L-R-C circuit. In this problem, you will consider a series L-R-C circuit, containing a resistor of resistance R, an inductor of inductance L, and a capacitor of capacitance C, all connected in series to an AC source providing an alternating voltage V(t) = V₁ cos(wt). (Figure 1) You may have solved a number of problems in which you had to find the effective resistance of a circuit containing multiple resistors. Finding the overall resistance of a circuit is often of practical interest. In this problem, we will start our analysis of this L-R-C circuit by finding its effective overall resistance, or impedance. The Vo impedance Z is defined by Z = where Vo and Io are the Io amplitudes of the voltage across the entire circuit and the current, respectively. Figure 1 of 2 AC source www soos C Review | Constants Part D What is the phase angle between the voltage and the current when resonance is reached? ► View Available Hint(s) 15. ΑΣΦ ? ø= Submit Part E Now imagine that the parameters R, L, w, and the amplitude of the voltage Vo are fixed but that the value of C can be changed. This is one of the easiest parameters to change when "tuning" such (radio frequency) circuits in order to make them resonate. This is because the capacitance can be changed just by moving the capacitor plates closer or farther apart. Find the capacitance Co at resonance. Express your answer in terms of L and w. —| ΑΣΦ ? Co = Submit Request Answer
Imagine that the parameters R, L, C, and the amplitude of the voltage V₁ are fixed, but the frequency of the voltage source is changeable. If the frequency of the source is changed from a very low one to a very high one, the current amplitude I will also change. The frequency at which I is at a maximum is called resonance. Find the frequency wo at which the circuit reaches resonance. Express your answer in terms of any or all of R, L, and C. ► View Available Hint(s) VE ΑΣΦ ? wo = Submit