Capacitive Reactance: Calculate Xc & V=I*Xc

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In summary, a pure capacitor C in an a.c. circuit has a voltage Vc of V0 * sin(w*t) and a charge Q of C * V0 * sin(w*t). The current I is the derivative of Q with respect to time, giving wCV0 sin(wt) as the expression for I. The relationship V = I * Xc is often used, with Xc being 1/(wC), but it is not a must to include complex numbers. The derivative of sin is cos, so it is not necessary to introduce imaginary roots. However, if considering the phase difference between voltage and current, it may be helpful to use complex numbers and the expression V = I * Xc * tan(w
  • #1
Devil Moo
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1
Hi,

A pure capacitor C is in an a.c. circuit.

Vc = V0 * sin(w*t)
Q = C * Vc
= C * V0 * sin(w*t)
I = dQ/dt
= wCV0 sin(wt)
then I0 = wCV0
Xc = V0 / I0 = 1/(wC)

So why people would say V = I * Xc?

Is it a must to include complex number?
 
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  • #2
The derivative of sin is cos.

You don't need complex numbers.
 
  • #3
Whoops!
I = I0 cos(wt)
Then V = I * Xc * tan(wt)
not V = I * Xc
 
  • #4
The relationship V=I*Xc (with real numbers) is between the amplitudes or rms values and not between instantaneous values.
Otherwise you need to consider Xc as a complex number, to take into account the phase difference between v and i.
 
  • #5
But why do we introduce imaginary root in it?
Is it used to describe the phase based on the e^(i*theta)?
 

1. What is capacitive reactance?

Capacitive reactance is the opposition to the flow of alternating current (AC) caused by the presence of a capacitor in a circuit. It is measured in ohms (Ω) and is inversely proportional to the frequency of the AC signal.

2. How do I calculate capacitive reactance (Xc)?

The formula for calculating capacitive reactance is Xc = 1/(2πfC), where f is the frequency of the AC signal in hertz and C is the capacitance of the capacitor in farads.

3. Can capacitive reactance be negative?

No, capacitive reactance cannot be negative. It is always a positive value since it represents the opposition to the flow of current in a circuit.

4. How does capacitive reactance affect the voltage in a circuit?

Capacitive reactance causes a phase shift between the voltage and current in a circuit. As the frequency of the AC signal increases, the capacitive reactance decreases, resulting in a decrease in the voltage across the capacitor.

5. How is capacitive reactance related to the current in a circuit?

Capacitive reactance is directly proportional to the current in a circuit. As the frequency of the AC signal increases, the capacitive reactance decreases, allowing more current to flow through the circuit.

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