The RLC series circuit illustrated in the Active Figure has R = 9.28 ?, and L =

Question

The RLC series circuit illustrated in the Active Figure has R = 9.28 ?, and L = 8.3 H . Suppose you want the circuit to respond most strongly at an applied frequency of? = 12.69 s-1. Find the capacitance that you should use.

Conceptualize
The rms current for a given applied AC voltage is determined by the impedance of the circuit, which in turn is determined by the resistance, impedance, and capacitance. The current is a maximum at the natural frequency of the circuit ?0 = 1/(LC)1/2.

Categorize
The problem involves applying the condition for resonance in an RLC circuit.

Analyze
The rms current is maximized at the natural frequency of the RLC circuit:

So the capacitance that is needed is:

Explanation / Answer

apply at resonance angular frequency W^2 = 1/LC

also W = 2pif

so

W = 2*3.14 * 12.69   = 79.69 rad/s

so

Capciatnce C = 1/W^2L

C = 1/(79.69 * 79.69 * 8.3)

C = 18.97 uF

-----------------------------------------------

Impedence Z^2 = R^2 +(XL-Xc)^2

at Resonance XL= XC

so

Z= R
so

Currenrt Irms = Vrms/R

Capciatnce C = 1/W^2L

C = 1/(79.69 * 79.69 * 8.3)

C = 18.97 uF

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.