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koban [17]
3 years ago
8

A capacitor of capacitance 102/π µF is connected across a 220 V, 50 Hz A.C. mains. Calculate the capacitive reactance, RMS value

of current and write down the equations of voltage and current.
Computers and Technology
1 answer:
Mademuasel [1]3 years ago
4 0

Answer:

The capacitive reactance will be "100Ω" and RMS value of current is "2.2 A". A further explanation is provided below.

Explanation:

Given:

C =\frac{10^2}{\pi}\times 10^{-6} \ F

V_{RMS}=220 \ V

f = 50 \ Hz

Now,

The capacitive reactance will be:

⇒ X_c=\frac{1}{\omega C} =\frac{1}{2 \pi f C}

                   =\frac{1}{2\times \pi\times 50\times \frac{10^{-4}}{\pi} }

                   =100 \ \Omega

RMS value of current will be:

⇒ I_{RMS}=\frac{V_{RMS}}{X_c}

             =\frac{220}{100}

             =2.2 \ A

So that,

⇒ V_m=220\times \sqrt{2}

         =311 \ V

⇒ I_m=2.2\times \sqrt{2}

         =3.1 \ A

hence,

The equation will be:

⇒ \nu=311 sin31 \ 4t

and,

⇒ i=3.1 sin(314t+\frac{\pi}{2} )

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