Calculating capacitive reactance

Thread Starter

Handymanjack

Joined Jun 20, 2011
9
Question : How does one calculate Xc when the capacitance is not known ? [ 2 unknowns in the equation].

Thanks, Jack
 

WBahn

Joined Mar 31, 2012
24,684
Question : How does one calculate Xc when the capacitance is not known ? [ 2 unknowns in the equation].

Thanks, Jack
Sounds like homework. Is it?

What equation are you referring to? What else is unknown besides the capacitance? There are several equations that involve capacitive reactance that could be used to calculated it.

What is the definition of reactance? That might give you an idea of one possible approach.
 

drc_567

Joined Dec 29, 2008
703
One method might consist of placing a resistor in series with a capacitor. Then apply an AC voltage across the two components, in series. The next productive step is to correctly visualize the mathematical arrangement of the two elements. They are in series, however, one component is mathematically real, and one component is mathematically imaginary.
 

Thread Starter

Handymanjack

Joined Jun 20, 2011
9
One method might consist of placing a resistor in series with a capacitor. Then apply an AC voltage across the two components, in series. The next productive step is to correctly visualize the mathematical arrangement of the two elements. They are in series, however, one component is mathematically real, and one component is mathematically imaginary.
Okay, good start. Please continue through the next steps.

Jack
 

drc_567

Joined Dec 29, 2008
703
The capacitive reactance is going to be the voltage across the capacitor divided by the series current. The series current is the current going through the resistor ... a real quantity, easy enough to calculate ... voltage drop division by resistance.
... The capacitor voltage, call it Vc, is going to be a result determined using the Pythagorean Theorem. The hypotenuse of the triangle is the total applied voltage, Vt. One known side of the triangle is a voltage measurement across the resistor, Vr. The unknown side of the triangle is Vc.
\[V_T^2=V_C^2+V_R^2\]
... You have found Vc and Ir.
 
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Thread Starter

Handymanjack

Joined Jun 20, 2011
9
The capacitive reactance is going to be the voltage across the capacitor divided by the series current. The series current is the current going through the resistor ... a real quantity, easy enough to calculate ... voltage drop division by resistance.
... The capacitor voltage, call it Vc, is going to be a result determined using the Pythagorean Theorem. The hypotenuse of the triangle is the total applied voltage, Vt. One known side of the triangle is a voltage measurement across the resistor, Vr. The unknown side of the triangle is Vc.
\[V_T^2=V_C^2+V_R^2\]
... You have found Vc and Ir.
Thank you; With your help, I'll attempt to answer my question.

Jack
 

Thread Starter

Handymanjack

Joined Jun 20, 2011
9
By the way. If all the AC measurements are taken at 60 Hz, would frequencies cancel and not be a consideration in the calculations ?

Jack
 

drc_567

Joined Dec 29, 2008
703
The particular frequency is not involved in the measurement of capacitive reactance.
A value for the frequency would be required to calculate the capacitance from the capacitive reactance, but not for the reactance itself.
 

BR-549

Joined Sep 22, 2013
4,936
"By the way. If all the AC measurements are taken at 60 Hz, would frequencies cancel and not be a consideration in the calculations ?"

Absolutely NOT!

I don't believe you understand what reactance is. In a resistor, the current goes thru it locked to the voltage across it. AS soon as the voltage changes......the current changes with it. This is Ohm's Law.

The current is locked and synchronized with the voltage. They are in "PHASE". Both happening at the same time.

Reactance KNOCKS the current out of phase with the voltage. The amount of knock depends on frequency. Or rate of change. NO CHANGE NO KNOCK. We can throw it off in two directions. We can delay the current with inductance reactance. And we can advance the current with capacitance reactance. In either case, the current is no longer matching the voltage in time. The amount of mis-match(reactance) is frequency dependent.

A voltage, current or multi meter measures averages. It can not see this phase difference. So your meter will lie to you. This is called apparent power.

But you can see the real-time difference with a scope. If you put the voltage in one channel and the current in another channel.....you can see the mismatch. It's kind of hard to put current into a scope. So if you put a resistor in series with cap.....the VOLTAGE DROP caused by resistor current, will be in phase with that cap current and NOT supply voltage. The resistor voltage is a copy in time of cap current. Does that make any sense? There is supply voltage.......and component voltage drop caused by current. This is why one circuit with one supply voltage.....can have many different voltages at different times....in a circuit. Different currents too.

Have I thoroughly confused you? Another important property of reactance is......it's square. It's physically perpendicular to the resistance. Impedance is the sum of a perpendicular.

This is where the trig and the Greeks come in. Adding a length to a sideways length. Or figuring the line of site distance of a square path.

Solving for Xc of a real circuit or component will require different methods than for solving an equation.

Sometimes Xc can be found from knowing a different parameter. Details make all the difference.
 

drc_567

Joined Dec 29, 2008
703
The reactance at one particular frequency would not be the same as the reactance at a different frequency. However, you should be able to make a determination of the reactance that is present in a simple series resistor-capacitor circuit, at one particular frequency.
 
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