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Impedances of R, L, C, RL, RC, LC and RLC circuits

  1. Dec 12, 2015 #1
    1. The problem statement, all variables and given/known data
    In first place, ignore the source in each circuit, ignore if make sense or not. I placed one sorce in each circuit just for the circuit be more visible.

    In second place, ignore the numerical values of the sources, resistors, capacitors and inductors. Think R, L and C in place of numerical values.

    So, my doubt is the following: given all these circuits, what is the equation of the impedeance (Z) in function of R, L and C?

    01.png

    02.png

    03.png

    2. Relevant equations


    3. The attempt at a solution

    1.1) Z = R
    1.2)
    1.3)

    2.1)
    2.2)
    2.3)
    2.4)
    2.5)
    2.6)

    3.1) Z = R + i(ωL - (ωC)⁻¹)
    3.2) Z = R⁻¹ + i(ωC - (ωL)⁻¹)
    3.3)
    3.4)
    3.5)
    3.6)
    3.7)
    3.8)
     
  2. jcsd
  3. Dec 12, 2015 #2

    Hesch

    User Avatar
    Gold Member

    ZR = R
    ZL = jωL
    ZC = 1 / jωC = j / (j*j*ωC) = -j / ωC

    In series you just add the impedances.
    In parallel use: Z = ( Z1-1 + Z2-1 + . . . )-1

    You must be able to calculate with complex numbers. Just remember that j2 = -1.

    Try to calculate 3.1) and 3.2) yourself ( think you have read the answer somewhere ).
     
    Last edited: Dec 12, 2015
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