NATURAL AND STEP RESPONSES OF RLC CIRCUITS

NATURAL AND STEP RESPONSES OF RLC CIRCUITS1

CLRI0iCiLiRv+_

L

R

C

t=0Iv+_2

The General Solution Of The Second-Order Differential Equation

3

4There are three possible outcomes

OverdampedUnderdampedCritically dampedThe Forms Of The Natural Response Of A Parallel RLC Circuit The Overdamped Voltage Response

5

The Underdamped Voltage response of a parallel RLC circuit is

The Critically Damped Voltage ResponseThe Underdamped Voltage Response

6The Step Response Of A Parallel RLC Circuit

RiRiLiCt=025nF25mHIv+_I=24mA, R=400Find iL(t) when t0I=24mA, R=625Find iL(t) when t0I=24mA, R=500Find iL(t) when t07

RiRiLiCt=0CLIv+_

Drill Exercises8

15V+_2.5F3k62.5HiLt=06k9mAFind iL(t) for t 09The Natural And Step Reponses Of A Series RLC Circuit

I0RLCiV0+_

10

11Find vC(t) for t 0Example12t=0-The Switch is opened

0.1H28048V0.4FvC++__t=0t=0+

13

t= The switch is closed

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Initial ConditionvC(0) =0

Drill Exercises

12.8k19.2k2FvC10mH100100Vi+_t=0+_50Vab+_Find v0(t) for t0Find vC(t) and i(t) for t015

781.25nF6k3k4k+_40V20V+_0.5Hv0(t)+_abt=0