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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 minimum time after which the current is in the same phase as that it was at t = 0 seconds,

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 minimum time after which the current is in the same phase as that it was at t = 0 seconds, Correct Answer 1 s

CONCEPT:

Phasors

  • A phasor is a vector that rotates about the origin with angular speed ω.

⇒ V = vm

⇒ I = im

  • The projection of voltage and current phasors on the vertical axis

⇒ Vy = vm sinωt

⇒ Iy = im sinωt

  • Phasors V and I for the case of a resistor are in the same direction. This means that the phase angle between the voltage and the current is zero. They rotate with frequency ω.

EXPLANATION:

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

At time t, the phase is given by ωt

  • The current repeats its phase after one oscillation
  • The time of one oscillation is T

⇒ T = 2π/ω = 1 s

  • Thus the time after which the current repeat its phase is 1 second. Therefore option 2 is correct.  

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