circuit analysis question

Question

The switch remains open for a long time and is ﻿closed at t = 0 . ﻿Find I_L ( t ) ﻿and V_L ( t ) ﻿for t ≥ 0 . ﻿Additionally, solve the problem i n ﻿the s - domain and t - domain.

Assam101 · Answer

1. initial conditions (before

t = 0

): the switch has been open for a long time, which means the circuit is in steady state. for an inductor in steady state, the current through it is constant, and the voltage across it is zero. voltage across the inductor:

v_l(0^-) = 0

current through the inductor:

i_l(0^-)

can be determined by the resistor network connected to the inductor. 2. at

t = 0^+

(after the switch closes): the circuit changes because the switch closes. the inductor resists sudden changes in current, so: initial current through the inductor:

i_l(0^+) = i_l(0^-)

voltage across the inductor:

v_l(0^+)

depends on the transient response. 3. find

i_l(t)

and

v_l(t)

for

\geq 0

: step a: equivalent circuit for

\geq 0

: when the switch closes, the circuit can be analyzed using: inductor impedance:

s l = 5 s

(in the laplace domain)use thevenin's theorem or direct circuit analysis to simplify the circuit. step b: differential equation in the time domain: apply kirchhoff's voltage law (kvl) around the loop containing the inductor:

v_{source} + v_r + v_l = 0

step c: laplace transform (s-domain): transform the circuit into the s-domain to solve for

i_l(s)

and

v_l(s)

, then perform an inverse laplace transform to find

i_l(t)

and

v_l(t)

.

tutormahima · Answer

answer to "circuit analysis question"

Anselmo · Answer

problema 23-2   fonte:    problema 7.35 - pag. 301    livro: análise de circuitos em engenharia - j. david irwin - 4ª edição - ed. pearson - 2013.

no circuito da figura 23-2.1 abaixo, a chave s ficou fechada por um longo período de tempo. para o tempo t = 0  a chave foi aberta. calcule a corrente i(t) para t ≥ 0.

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circuit analysis question

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