Peak Current of 0.03\mu F Capacitor on 2kV, 720Hz Line

In summary, the peak value of the current of a 0.03\mu F capacitor connected to a 2.0-kV(rms) 720-Hz line is 2.7 * 10^{-1} A. However, to obtain the peak value, this must be multiplied by sqrt(2) to account for the maximum amplitude of a sinusoidal function. The rms value is the root mean square value of all individual values, and is equal to the peak value divided by sqrt(2).
  • #1
leolaw
85
1
I am always confused with rms value and peak value, so here is the problem:

What will be the peak value of the current of a well-insulated [tex]0.03\mu F[/tex] capacitor connected to a 2.0-kV(rms) 720-Hz line?

So first I find the reactance of the capacitor, which is:
[tex]X_c=\frac{1}{2\pi fC}[/tex]
[tex]7.4k \Omega[/tex]

and then [tex]V_{rms} = I_rms * X_c[/tex]
[tex] 2*10^3 = I_{rms} (7.4 * 10^3)[/tex]
[tex] I_{rms} = 2.7 * 10^{-1} A[/tex]

so is this the right answer, or do i have to multiply it by [tex]\sqrt{2}[/tex] to get the peak value?
 
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  • #2
leolaw said:
I am always confused with rms value and peak value, so here is the problem:

What will be the peak value of the current of a well-insulated [tex]0.03\mu F[/tex] capacitor connected to a 2.0-kV(rms) 720-Hz line?
...
[tex] I_{rms} = 2.7 * 10^{-1} A[/tex]

so is this the right answer, or do i have to multiply it by [tex]\sqrt{2}[/tex] to get the peak value?


The peak value is sqrt(2) times the rms value, and the peak was asked...


ehild
 
  • #3
Yes he is correct. Since current can be described in the form of a sin fn, the maximum amplitude obtained is known as peak value. rms value is the root mean square value of all individual values

For eg, peak value of sin(x) is 1. But it takes values from -1 to 1. rms value=1/sqrt(2).
It is the net effect.
 

Related to Peak Current of 0.03\mu F Capacitor on 2kV, 720Hz Line

What is the significance of the peak current in a capacitor?

The peak current in a capacitor refers to the maximum amount of current that flows through the capacitor during a charging or discharging cycle. It is an important factor in determining the power handling capability and efficiency of a capacitor.

How does the size of a capacitor affect its peak current?

The peak current of a capacitor is directly proportional to its capacitance. This means that a larger capacitor will have a higher peak current compared to a smaller capacitor, assuming they are both charged to the same voltage.

What is the relationship between the voltage and peak current of a capacitor?

The peak current of a capacitor is directly proportional to the charging voltage. This means that as the voltage increases, the peak current also increases. However, the peak current will eventually reach a limit known as the "saturation current" when the capacitor is fully charged.

How does the frequency of the line affect the peak current of a capacitor?

The peak current of a capacitor is inversely proportional to the frequency of the line. This means that as the frequency increases, the peak current decreases. This is because a higher frequency allows for faster charging and discharging of the capacitor, resulting in a lower peak current.

What are the potential risks of using a capacitor with a peak current of 0.03\mu F on a 2kV, 720Hz line?

Using a capacitor with a peak current of 0.03\mu F on a 2kV, 720Hz line can be risky as it may lead to overloading and damage to the capacitor. It is important to ensure that the capacitor is rated for the specific voltage and frequency of the line to avoid any potential hazards.

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