In an AC circuit with resistance R = 1 Ω and oscillating potential v = vm sinωt, where vm = 1 V and ω = 2π rad/s, the value of average current in time t ∈ [0 s, 0.5 s] is,

  

CONCEPT:

• The oscillating potential of an AC circuit is given by

⇒ v = vm sinωt

where 'vm' is the amplitude of the oscillating potential difference and 'ω' is the angular frequency

• The oscillating current in an AC circuit is given by

where 'i' is the amplitude of the oscillating current

since 'vm' and 'R' are constants, 

⇒ i = im sinωt

where 

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EXPLANATION:

Given: resistance R = 1 Ω, oscillating potential v = vm sinωt, where vm = 1 V and ω = 2π rad/s

• The oscillating potential of an AC circuit is given by

⇒ v = vm sinωt

where 'vm' is the amplitude of the oscillating potential difference and 'ω' is the angular frequency

• The oscillating current in an AC circuit is given by

where 'i' is the amplitude of the oscillating current

• The average current over a half sinusoidal cycle is

• ​Therefore option 1 is correct.