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

1. Dec 12, 2015

Bruno Tolentino

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?

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. Dec 12, 2015

Hesch

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