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

[Bruno Tolentino]

Homework Statement

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?

Homework Equations

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)

 

[Hesch]

Z_R = R
Z_L = jωL
Z_C = 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 ).