# Resistors, Inductors, and Capacitors

1- Assume a passive network N composed of resistors, inductors, and capacitors

A- How can you modify N such that each and every natural frequency is shifted one unit to left? (i.e. its real part is reduced by 1)

B- How can you modify N such that each and every natural frequency is shifted one unit to right? (i.e. its real part is increased by 1)

https://brainmass.com/physics/resistors/resistors-inductors-capacitors-14849

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please find the solution in the attachment.

In this problem, you are basically asked to find out how can you affect N so that resonance can be altered.

Since for a RLC circuit, the resonant frequency is given by

Wo = 1/ sqrt (LC)

Since in your case, it's a network of N, equation becomes

Wo = 1/ N sqrt (LC) ----------------------ïƒ (1)

Case 1)

To reduce the natural frequency by changing N, (keeping RLC unchanged)

W1 = 1/ N' sqrt (LC) --------------------------ïƒ (2)

Dividing (1) by (2), we have

So, N' = N ( Wo/ W1)

But W1 = W0 - 1

Hence N' = N ( Wo / Wo - 1)

Increase the Number of RLCs by N'

Case (2)

Here W1 = W0 + 1

Hence N' = N ( Wo / Wo + 1)

Reduce the number of RLCs by N'

Aside : for RLC,

Output impedance Z = sqrt ( R^2 + (Xl - Xc) ^2)

At resonance Xl = Xc so that Z = R; which leads us to the resonance frequency

Wo = 1/ sqrt (LC) ; ( Xl = j WL ; Xc = 1/j W c )

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