Understanding Z(in) of Circuit: A, B, C, D Explained [No Frequency Given]

[asdf12312]

Z(in) of circuit help??

Homework Statement

A. 10+j2.5 (Ω)
B. 10-j0.4 (Ω)
C. 10-j2.5 (Ω)
D. 10+j0.4 (Ω)

Homework Equations

Z(L)=jwl
Z(C)=-j/wc

The Attempt at a Solution

the problem asks for z(in) without any frequency w given? i think i was just confused by the wording of this problem. s=sigma+jw so does that mean, j2 given means w=2?? then answer would be 10+j2.5 (A). but I'm unsure how to do this without any w.

 

[berkeman]

Yeah, it looks like they are asking for Z(w=j2), so j2 must be the frequency w. 2Hz shifted by 90 degrees...?

 

[TimeToShine]

Remember your transfer function can be expressed in the form H(jω) = Vo(jω)/Vi(jω), where we can denote jω by s.

Here you are trying to find the input impedance Z(i), or in other words Z(jω), where Z(jω) = Z(2j).

So you can conclude that ω = 2 rad/s or ω = 2*pi*f = 2 and find the frequency.

Find the total impedance of the system and substitute your value of ω.

 

[NascentOxygen]

The general expression is V(s). To express in the frequency domain, we simply substitute s with jω, giving V(jω)

So V(j2) indicates V(jω) with ω=2 radians/sec.