How Does Increasing Frequency Affect Current, Voltage, and Impedance (Z)?

AI Thread Summary
Increasing frequency in a circuit leads to an increase in current amplitude, which results in a decrease in impedance (Z) when voltage (V) remains constant. The relationship V = I*Z highlights this inverse relationship. Discussions also touch on the behavior of impedance in a series RLC circuit, particularly at low (ω→0) and high frequencies (ω→∞). Participants express uncertainty about sketching impedance graphs and suggest reviewing relevant equations and online resources for clarity. Understanding these dynamics is crucial for analyzing circuit behavior across different frequencies.
hidemi
Messages
206
Reaction score
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?
 
Physics news on Phys.org
What are 6-png.282284, etc. Did you miss posting some figures?
 
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?
 
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.
 
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.
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top