Question

A 0.74 mF capacitor is connected to a standard outlet (rms voltage 82 V, frequency 49 Hz ). Determine the magnitude of the current in the capacitor at t

Answer 1

Answer:

I =  26.36 cosω t A

Explanation:

Given that

C=0.74 mF

Vrms= 82 V

Frequency ,f= 49 Hz

We know that ω = 2 π f

ω = 2 x  π x 49

ω = 307.72 rad/s

As we know that voltage given as

V= Vo sinω t

$V_o=\sqrt2\ V_{rms}$

$V_o=\sqrt2\ \times 82$\

Vo=115.96 V

V=115.96 sinω t

The current given as

$I=C\dfrac{dV}{dt}$

$I=0.74\times \dfrac{dV}{dt}\ mA$

$\dfrac{dV}{dt}=115.96\omega cos\omega t$

$I=0.74\times 115.96\times 307.22 cos\omega t\ mA$

I = 26362.67 cosω t mA

I =  26.36 cosω t A

This is the current at time ant time t.