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Homework Help: Find v(t) and i(t) in the RC circuit

  1. Nov 1, 2016 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations
    Voltage Division
    v2 = vs * (r2/(r2+r1))
    KCL - sum of all currents at a given node is 0
    V= i * r

    3. The attempt at a solution

    This is my solution:

    This is my professor's solution:

    I understand finding v(t) but when it comes to i(t) I'm confused.
    First conceptual question:
    I know the current across an inductor must be continuous at t = 0 but does this also apply to the current through a capacitor at t = 0? I imagine this isn't the case since neither me or the professor's solution point to this.

    Next question, how is 0 mA the answer for t<0 ? If the switch is closed during this time then there should still be a current going down that path.
    Was my approach for finding i(t) when t<0 incorrect? I drew the circuit for t<0, under DC regime a capacitor can be treated as an open circuit, I found Rth and found the current of that circuit. Wouldn't the current of that circuit be i(t) for t<0?

    I know I asked a lot of questions so answering any part of it, if not all, would still be extremely helpful.
    Thanks in advance!
    Last edited: Nov 1, 2016
  2. jcsd
  3. Nov 2, 2016 #2


    User Avatar
    Homework Helper
    Gold Member

    No. Capacitor current can change instantaneously, which prevents the voltage across the capacitor to change instantaneously. Capacitor resists sudden changes in the voltage across it.
    I believe you are expected to assume i(t) as the capacitor current. Hence for t<0, it is 0.
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