Verification of the capacitance of a capacitor

[Samar A]

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.

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.

Is it correct?

 

[cnh1995]

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?).

 

[Samar A]

Conductance is the reciprocal of resistance. What you have in the circuit is a capacitor (or condenser).

Oh, sorry, I corrected it.

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?

 

[cnh1995]

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.