# Electronics/RCL

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## RLC Series

editAn RLC series circuit consists of a resistor, inductor, and capacitor connected in series:

By Kirchhoff's voltage law the differential equation for the circuit is:

or

Leading to:

- ±

with

- and

There are three cases to consider, each giving different circuit behavior, .

- .
- =

Equation above has only one real root

- s = -α =

- ,
- >

Equation above has only two real roots

- ±

- .

Equation above has only two complex roots

- + j
- - j

## Circuit Analysis

edit### R = 0

editIf R = 0 then the RLC circuit will reduce to LC series circuit . LC circuit will generate a standing wave when it operates in resonance; At Resonance the conditions rapidly convey in a steady functional method.

### R = 0 Z_{L} = Z_{C}

edit
If R = 0 and circuit above operates in resonance then the total impedance of the circuit is Z = R and the current is V / R

At Resonance

- Or

At Frequency

- I = 0 . Capacitor opens circuit . I = 0
- I = 0 Inductor opens circuit . I = 0

Plot the three value of I at three I above we have a graph I - 0 At Resonance frequency the value of current is at its maximum . If the value of current is half then circuit has a stable current does not change with frequency over a Bandwidth of frequencies É1 - É2 . When increase current above circuit has stable current over a Narrow Bandwidth . When decrease current below circuit has stable current over a Wide Bandwidth

Thus the circuit has the capability to select bandwidth that the circuit has a stable current when circuit operates in resonance therefore the circuit can be used as a Resonance Tuned Selected Bandwidth Filter