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Homework Help: AC circuit

  1. Aug 3, 2010 #1
    1. The problem statement, all variables and given/known data

    A resistor of resistance R is connected to an AC
    generator with EMF(t)=(EMF_max)sin((w_d)t). (a) Write
    Kirchhoff's Loop Rule for this circuit at a particular
    instant of time. Is your result a differential equation?
    (b) Find the current as a function of time. Now assume
    R=50 Ohm and EMF_max = 30.0 V. (c) What is the amplitude
    of the resulting alternating current if the frequency of
    the EMF is 1.00 kHz?

    2. Relevant equations

    V_R = R dQ(t)/dt

    3. The attempt at a solution

    Ok, so the differential equation I came up with is:
    V_G + V_R = 0
    E_m sin(w_d t) = R dQ(t)/dt

    assuming thats correct how do I find the current as a function of time? Replace dq/dt with i? And after that?
     
  2. jcsd
  3. Aug 4, 2010 #2

    Delta²

    User Avatar
    Homework Helper
    Gold Member

    And after that u get equation [tex]E_m sin(w_d t)=R I[/tex], hence [tex]I=\frac {E_m sin(w_d t)}{R}[/tex] and the amplitude of the ac current is [tex]\frac{E_m}{R}[/tex]

    Something else, usually we apply Kirchoff's Law with currents and voltages and not with charges Q. Therefore MAYBE the correct answer to a) is by having replace dq/dt with I from the start and therefore the equation isnt a differential equation.
     
    Last edited: Aug 4, 2010
  4. Aug 4, 2010 #3
    Perfect, thank you!
     
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