Thank you for visiting A capacitor of capacitance tex frac 102 pi mu F tex is connected across a 220 V 50 Hz A C mains Calculate the capacitive. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer:
The capacitive reactance will be "100Ω" and RMS value of current is "2.2 A". A further explanation is provided below.
Explanation:
Given:
[tex]C =\frac{10^2}{\pi}\times 10^{-6} \ F[/tex]
[tex]V_{RMS}=220 \ V[/tex]
[tex]f = 50 \ Hz[/tex]
Now,
The capacitive reactance will be:
⇒ [tex]X_c=\frac{1}{\omega C} =\frac{1}{2 \pi f C}[/tex]
[tex]=\frac{1}{2\times \pi\times 50\times \frac{10^{-4}}{\pi} }[/tex]
[tex]=100 \ \Omega[/tex]
RMS value of current will be:
⇒ [tex]I_{RMS}=\frac{V_{RMS}}{X_c}[/tex]
[tex]=\frac{220}{100}[/tex]
[tex]=2.2 \ A[/tex]
So that,
⇒ [tex]V_m=220\times \sqrt{2}[/tex]
[tex]=311 \ V[/tex]
⇒ [tex]I_m=2.2\times \sqrt{2}[/tex]
[tex]=3.1 \ A[/tex]
hence,
The equation will be:
⇒ [tex]\nu=311 sin31 \ 4t[/tex]
and,
⇒ [tex]i=3.1 sin(314t+\frac{\pi}{2} )[/tex]
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