Learning Goal: To understand the use of phasor diagrams in calculating the imped

Question

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 , an inductor of inductance , and a capacitor of capacitance , all connected in series to an AC source providing an alternating voltage . (Intro 1 figure)

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 impedance is defined by , where and are the amplitudes of the voltage across the entire circuit and the current, respectively.

You may find the following reminders helpful:

Explanation / Answer

the impedance, Z is found from

Z = sqrt(R2 + (XL - XC)2)

Z = sqrt(R2 + (L - 1/C)2)

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