Exploring Current, Voltage & Z When Frequency Increases

In summary, the conversation discusses the relationship between increasing frequency, current amplitude, and impedance in a series RLC circuit. The group agrees that if frequency increases, current amplitude increases, and impedance decreases due to the equation V = I*Z. They also discuss the significance of ω→0 and ω→∞ in relation to impedance. However, they are unsure how to sketch a graph of impedance magnitude versus frequency and mention the need for more information or equations to do so accurately.
  • #1
hidemi
208
36
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?
 
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  • #2
What are 6-png.282284, etc. Did you miss posting some figures?
 
  • #3
Yes, the 2nd half of your post isn't working.
hidemi said:
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?
 
  • Like
Likes hutchphd
  • #4
DaveE said:
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.
 
  • #5
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.
 

FAQ: Exploring Current, Voltage & Z When Frequency Increases

What is the relationship between current, voltage, and frequency?

The relationship between current, voltage, and frequency is described by Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage and inversely proportional to the resistance. This means that as frequency increases, the current and voltage also increase, assuming the resistance remains constant.

How does increasing frequency affect the impedance (Z) of a circuit?

As frequency increases, the impedance of a circuit also increases. This is because impedance is a measure of the total opposition to current flow in a circuit, and at higher frequencies, there is more opposition due to factors such as inductance and capacitance.

What is the significance of exploring current, voltage, and Z when frequency increases?

Exploring the relationship between current, voltage, and Z when frequency increases is important in understanding the behavior of electrical circuits and devices. It can help in designing and troubleshooting circuits, as well as predicting the performance of electronic components at different frequencies.

How do current, voltage, and Z change in a series circuit as frequency increases?

In a series circuit, as frequency increases, the current and voltage both increase, while the impedance also increases. This is because the components in a series circuit have a cumulative effect on the overall impedance, and at higher frequencies, this effect becomes more pronounced.

How can we measure the changes in current, voltage, and Z as frequency increases?

The changes in current, voltage, and Z as frequency increases can be measured using various instruments such as multimeters, oscilloscopes, and frequency generators. These instruments can provide accurate readings of current, voltage, and impedance at different frequencies, allowing for a comprehensive analysis of the circuit's behavior.

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