An alternating voltage (in volts) given ...

An alternating voltage (in volts) given by `V=200sqrt(2)sin(100t)` is connected to `1 mu F` capacitor through an ideal ac ammeter in series. The reading of the ammeter and the average power consumed in the circuit shall be

20 mA, 0

20 mA, 4W

`20sqrt(2)mA, 8W`

`20sqrt(2)mA, 4sqrt(2)W`

Text Solution

Verified by Experts

The correct Answer is:

On comparing `V = 200sqrt(2)sin(100 t)` with
`V = V_(0)sin omega t`, we get
`V_(0)=200sqrt(2) V, omega = 100" rad " s^(-1)`
`therefore V_("rms")=(V_(0))/(sqrt(2))=(200sqrt(2)V)/(sqrt(2))=200 V`
The capacitive reactance is
`X_(C )=(1)/(omega C)=(1)/(100xx1xx10^(-6))=10^(4)Omega`
ac ammeter reads teh rms value of current. Therefore, the reading of the ammeter is
`I_("rms")=(V_("rms"))/(X_(C ))=(200 V)/(10^(4)Omega)=20xx10^(-3)A=20 mA`
The average power consumedin the circuit,
`P = I_("rms")V_("rms")cos phi`
In an pure capacitive circuit, the phase difference between current and voltage is `(pi)/(2)`.
`therefore cos phi = 0 therefore P = 0`

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