A parallel plate capacitor made to circular plates each of radius R=6 cm has capacitance C=100

step 1 In this problem I can write the value of iRMS is equal to ERMS by XC which can be further writte

A parallel plate capacitor made to circular plates each of...

A parallel plate capacitor made to circular plates each of radius $R=6 \mathrm{~cm}$ has capacitance $C=100 \mathrm{pF}$. The capacitance is connected to a $230 \mathrm{~V}$ AC supply with an angular frequency of $300 \mathrm{rad} / \mathrm{s}$. The rms value of conduction current will be (A) $5.7 \mu \mathrm{A}$ (B) $6.3 \mu \mathrm{A}$ (C) $9.6 \mu \mathrm{A}$ (D) $6.9 \mu \mathrm{A}$

A parallel plate capacitor made to circular plates each of radius $R=6 \mathrm{~cm}$ has capacitance $C=100 \mathrm{pF}$. The capacitance is connected to a $230 \mathrm{~V}$ AC supply with an angular frequency of $300 \mathrm{rad} / \mathrm{s}$. The rms value of conduction current will be
(A) $5.7 \mu \mathrm{A}$
(B) $6.3 \mu \mathrm{A}$
(C) $9.6 \mu \mathrm{A}$
(D) $6.9 \mu \mathrm{A}$

Key Concepts

Capacitance

Capacitance is the property of a capacitor to store electrical energy by means of an electric field established between its conductors. In AC circuits, the capacitor’s value, together with the angular frequency of the source, determines how easily the capacitor can allow current to flow through it.

Capacitive Reactance

Capacitive reactance is the measure of a capacitor's opposition to alternating current, calculated as X_C = 1/(?C). It quantifies how a capacitor impedes AC at a given angular frequency, which is crucial for determining the current that flows in response to an applied voltage.

Angular Frequency

Angular frequency (?) represents the rate of change of the sinusoidal waveform and is expressed in radians per second. It connects the time domain behavior of AC signals with circuit parameters like reactance, having a direct influence on the capacitor's impedance.

RMS Value

The RMS (root-mean-square) value is a statistical measure of the magnitude of a varying quantity and, in AC circuits, corresponds to the equivalent DC value that would produce the same power dissipation. This concept is vital when calculating effective current and voltage in AC circuits.

AC Circuit Analysis

AC circuit analysis involves evaluating the behavior of circuits powered by alternating current, including the phase relationships between voltage and current, and the complex impedance presented by reactive components like capacitors. This analysis is essential for understanding power distribution and signal behavior in AC electrical systems.

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