Exploring Current, Voltage & Z When Frequency Increases

[hidemi]

Homework Statement

An RLC series circuit is driven by a sinusoidal emf with angular frequency ωd. If ωd is increased without changing the amplitude of the emf the current amplitude increases. If L is the inductance, C is the capacitance, and R is the resistance, this means that:

A.ωdL >1/ωdC
B.ωdL <1/ωdC
C.ωdL= 1/ωdC
D.ωdL > R
E.ωdL < R

The answer is B.

Relevant Equations

(see better expression below)

https://www.physicsforums.com/attachments/6-png.282284/?hash=0362cb24c9a8ed9b3ee9efab56a28e3d
If the increasing frequency leads the current amplitude to increases, then Z decreases because V = I*Z and V remains unchanged.

https://www.physicsforums.com/attachments/7-png.282286/?hash=0362cb24c9a8ed9b3ee9efab56a28e3d
must decrease, so

https://www.physicsforums.com/attachments/7-png.282288/?hash=0362cb24c9a8ed9b3ee9efab56a28e3d is equal to 0.

so I think the answer should be C not B. Where am I wrong?

 

[kuruman]

What are 6-png.282284, etc. Did you miss posting some figures?

 

[DaveE]

Yes, the 2nd half of your post isn't working.

If the increasing frequency leads the current amplitude to increases, then Z decreases because V = I*Z and V remains unchanged.

Yes.

Can you sketch a graph of the impedance magnitude of a series RLC versus frequency?
What is the impedance as ω→0, and ω→∞?
What is/are the significant frequencies in that sketch?

 

[hidemi]

Yes, the 2nd half of your post isn't working.

Yes.

Can you sketch a graph of the impedance magnitude of a series RLC versus frequency?
What is the impedance as ω→0, and ω→∞?
What is/are the significant frequencies in that sketch?

We didn't discuss how to draw that in class, so I am not sure how.

 

[kuruman]

Did you discuss the equation relating the current to the frequency in a series RLC circuit? If not, there are numerous links on the web including plots that should help with this question. Alternatively, if you have the equation, take its derivative with respect to the frequency and see what condition must be satisfied to have the current increase with frequency. Or, as @DaveE suggested, see what happens at the two limits when the frequency is relatively small and relatively large.