Question 144: AC fundamentals

Question

A parallel plate capacitor has a capacitance $\mathrm{C}=200~ \mathrm{pF}$. It is connected to $230 \mathrm{~V}$ ac supply with an angular frequency $300~ \mathrm{rad} / \mathrm{s}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

Accepted Answer

To solve this problem, we need to understand how to calculate the rms current in an AC circuit containing a capacitor, as well as the concept of displacement current.
First, the rms (root mean square) value of the current ($I_{	ext{rms}}$) in a capacitor when connected to an AC supply is given by:
$I_{	ext{rms}} = V_{	ext{rms}} \cdot \omega C$
where $V_{	ext{rms}}$ is the rms voltage, $\omega$ is the angular frequency, and $C$ is the capacitance.
For an AC supply, the rms voltage is related to the peak voltage ($V_0$) by:
$V_{	ext{rms}} = \frac{V_0}{\sqrt{2}}$
However, we've been given the rms voltage directly, which is $230\, 	ext{V}$. Therefore, we can use this value directly in our calculations.
Given:
$C = 200\, 	ext{pF} = 200 	imes 10^{-12}\, 	ext{F}$
$\omega = 300\, 	ext{rad/s}$
$V_{	ext{rms}} = 230\, 	ext{V}$
Substitute these values into the equation for rms current:
$I_{	ext{rms}} = V_{	ext{rms}} \cdot \omega C = 230 	imes 300 	imes 200 	imes 10^{-12} = 13.8 	imes 10^{-6}\, 	ext{A}$
Therefore, the rms value of the conduction current is $13.8\, \mu 	ext{A}$.
Now, for the displacement current (which is essentially the current that would "flow" through the dielectric of the capacitor as a result of the changing electric field). In an AC circuit, the displacement current and the conduction current are the same. That's because the displacement current is necessary to sustain the changing electric field between the plates of the capacitor, and this changing field is what causes the conduction current in the leads and the rest of the circuit.
Hence, the rms value of the displacement current is the same as the conduction current, which is $13.8\, \mu 	ext{A}$.
So, the correct option is:
Option B
$13.8\, \mu 	ext{A}$ and $13.8\, \mu 	ext{A}$

Answer

$14.3 ~\mu \mathrm{A}$ and $143 ~\mu \mathrm{A}$

Answer

$13.8 ~\mu \mathrm{A}$ and $13.8 ~\mu \mathrm{A}$

Answer

$13.8 ~\mu \mathrm{A}$ and $138 ~\mu \mathrm{A}$

Answer

$1.38 ~\mu \mathrm{A}$ and $1.38 ~\mu \mathrm{A}$

AC fundamentals

A parallel plate capacitor has a capacitance \mathrm{C}=200~ \mathrm{pF}. It is connected to 230 \mathrm{~V} ac supply with an angular frequency 300~ \mathrm{rad} / \mathrm{s}. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

Choose the correct answer: