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

I = 26.36 cosω t A

Step-by-step 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\ * 82`\

Vo=115.96 V

V=115.96 sinω t

The current given as

`I=C(dV)/(dt)`

`I=0.74* (dV)/(dt)\ mA`

`(dV)/(dt)=115.96\omega cos\omega t`

`I=0.74* 115.96* 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.