Final answer:
The RMS current flowing through a parallel plate capacitor with a capacitance of 200 pF connected to a 230 V supply with an angular frequency of 400 rad/s is approximately 2.88 mA.
Step-by-step explanation:
The root mean square (RMS) current in a capacitor connected to an AC voltage supply can be calculated using the formula for capacitive reactance (XC) and the RMS voltage. The capacitive reactance is given by XC = ýiv>(wC), where ö is the angular frequency in rad/s, and C is the capacitance in farads. The RMS current (IRMS) can be found using Ohm's law for AC circuits: IRMS = VRMS ýiv> XC.
Given a capacitor with a capacitance of 200 pF (which is 200 x 10-12 F) and an AC supply with an RMS voltage of 230 V and an angular frequency of 400 rad/s, first calculate the capacitive reactance:
XC = ýiv>(wC) = 1 ýiv> (400 rad/s x 200 x 10-12 F) = 1 ýiv> (80 x 10-6) Ω
Now, calculate the RMS current:
IRMS = VRMS ýiv> XC = 230 V ýiv> (1 ýiv> (80 x 10-6)) A ≈ 2.88 mA