Verification of the capacitance of a capacitor

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Homework Help Overview

The discussion revolves around verifying the capacitance of a capacitor in a circuit where the phase difference between current and voltage is initially 30 degrees, with the goal of adjusting it to 15 degrees. The subject area includes concepts related to capacitors, phase differences in AC circuits, and the relationship between capacitance and reactance.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the mathematical relationship between phase difference, reactance, and resistance, questioning the correctness of the original poster's approach. There is exploration of why an increase in capacitance would lead to a smaller phase difference.

Discussion Status

Some participants have provided guidance on the relationship between capacitance and phase difference, noting that an increase in capacitance results in decreased capacitive reactance. Multiple interpretations of the problem are being explored, particularly regarding the effects of capacitance on phase difference.

Contextual Notes

There is a mention of potential confusion between conductance and capacitance, indicating a need for clarification on terminology. The original poster's values and specific calculations have not been verified step by step, leaving some assumptions open for discussion.

Samar A
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Homework Statement


In the circuit shown in the figure below, the hase difference between the current and the voltage is 30 degrees, show how could you verify the capacitance of the conductor so that the phase difference could be 15 degrees.
Muz9U.jpg

Homework Equations


tan θ=-Xc/R (the phase difference in the RC cirucit with an AC source)

The Attempt at a Solution


That is my attempt, I show how much would be the value of the capacitance in the second case mathematically.
2VX1D.png

Is it correct?
 
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Samar A said:
show how could you verify the conductance **capacitance** of the conductor so that the phase difference could be 15 degrees.
Conductance is the reciprocal of resistance. What you have in the circuit is a capacitor (or condenser).
I didn't check your actual values step by step, but your approach is correct. Also, the new capacitance is coming out to be more than the old capacitance, which is correct (can you think why?).
 
cnh1995 said:
Conductance is the reciprocal of resistance. What you have in the circuit is a capacitor (or condenser).
Oh, sorry, I corrected it.
cnh1995 said:
can you think why?).
OK, I think because when the capacitance is greater the reactance of the capacitor will be less than the original one, so its effect in the circuit will be smaller, and then the phase difference between the current and the voltage will be smaller too. Am I right?
 
Samar A said:
OK, I think because when the capacitance is greater the inductance **reactance** of the capacitor will be less than the original one, so its effect in the circuit will be smaller, and then the phase difference between the current and the voltage will be smaller too. Am I right?
Right. Capacitive reactance is inversely proportional to the capacitance.
 
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