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In an AC circuit, if the voltage is given by V(t) = V0 sin(ωt), what is the expr

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Question: In an AC circuit, if the voltage is given by V(t) = V0 sin(ωt), what is the expression for the current if the circuit is purely inductive? (2023)

Options:

  1. I(t) = I0 sin(ωt)
  2. I(t) = I0 sin(ωt - π/2)
  3. I(t) = I0 cos(ωt)
  4. I(t) = I0 cos(ωt + π/2)

Correct Answer: I(t) = I0 sin(ωt - π/2)

Exam Year: 2023

Solution: 

In a purely inductive circuit, the current lags the voltage by 90 degrees (π/2 radians). Therefore, I(t) = I0 sin(ωt - π/2).

In an AC circuit, if the voltage is given by V(t) = V0 sin(ωt), what is the expr

Practice Questions

Q1
In an AC circuit, if the voltage is given by V(t) = V0 sin(ωt), what is the expression for the current if the circuit is purely inductive? (2023)
  1. I(t) = I0 sin(ωt)
  2. I(t) = I0 sin(ωt - π/2)
  3. I(t) = I0 cos(ωt)
  4. I(t) = I0 cos(ωt + π/2)

Questions & Step-by-Step Solutions

In an AC circuit, if the voltage is given by V(t) = V0 sin(ωt), what is the expression for the current if the circuit is purely inductive? (2023)
  • Step 1: Understand that in an AC circuit, voltage can be expressed as V(t) = V0 sin(ωt), where V0 is the maximum voltage, ω is the angular frequency, and t is time.
  • Step 2: Recognize that in a purely inductive circuit, the current does not change instantaneously with the voltage. Instead, it lags behind the voltage.
  • Step 3: Know that the current lags the voltage by 90 degrees, which is equivalent to π/2 radians.
  • Step 4: To express the current I(t), we start with the voltage expression and adjust it for the phase difference. Since the current lags, we subtract π/2 from the voltage's angle.
  • Step 5: Write the expression for the current as I(t) = I0 sin(ωt - π/2), where I0 is the maximum current.
  • AC Circuit Behavior – Understanding how voltage and current behave in an alternating current (AC) circuit, particularly in inductive components.
  • Phase Relationship – Knowledge of the phase difference between voltage and current in a purely inductive circuit, where current lags voltage by 90 degrees.
  • Sine Wave Functions – Ability to manipulate and understand sine wave functions in the context of AC circuits.
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