A 15.0 μ F capacitor is connected to a 220 V , 50 Hz source. capacitive reactance and current ( rms

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7.Alternating Current

medium

A $15.0 \;\mu$ F capacitor is connected to a $220\; V , 50 \;Hz$ source. Find the capacitive reactance and the current ($rms$ and peak) in the circuit. If the frequency is doubled, what happens to the capacitive reactance and the current?

Option A

Option B

Option C

Option D

Solution

The capacitive reactance is

$X_{C}=\frac{1}{2 \pi v C}=\frac{1}{2 \pi(50 Hz )\left(15.0 \times 10^{-6} F \right)}=212 \Omega$

The $rms$ current is

$I=\frac{V}{X_{C}}=\frac{220 V }{212 \Omega}=1.04 A$

The peak current is

$i_{m}=\sqrt{2} I=(1.41)(1.04 A)=1.47 A$

This current oscillates between $+1.47 A$ and $-1.47 A ,$ and is ahead of the voltage by $\pi / 2$ If the frequency is doubled, the capacitive reactance is halved and consequently, the current is doubled.

Standard 12

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normal

(IIT-2012)

A $15.0 \;\mu$ F capacitor is connected to a $220\; V , 50 \;Hz$ source. Find the capacitive reactance and the current ($rms$ and peak) in the circuit. If the frequency is doubled, what happens to the capacitive reactance and the current?

Solution

Similar Questions

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