Question

An alternating voltage e = `200sqrt2` sin(100 t) volt is connected to a 1 µF capacitor through a.c. ammeter. The reading of the ammeter is ______

Options

• 5 mA

• 10 mA

• 15 mA

• 20 mA

Answer 1

An alternating voltage e = `200sqrt2` sin(100 t) volt is connected to a 1 µF capacitor through a.c. ammeter. The reading of the ammeter is 20 mA.

Explanation:

Alternating voltage: e = `200sqrt2` sin(100 t) volt

Comparing with e = e₀ sin ωt 

ω = 100 rad/s, e₀ = `200sqrt2`

Capacitive reactance,

X_C = `1/(omega"C") = 1/(100 xx 10^-6)Omega = 10^4Omega`

`"I"_0 = "e"_0/"X"_"c"`

`"I"_0 = (200sqrt2)/10^4`

`"I"_0 = 2sqrt2 xx 10^-2` A

`"I"_"rms" = "I"_0/sqrt2 = (2sqrt2 xx 10^-2)/(sqrt2) = 2 xx 10^-2` A = 20 mA