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)

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Q: 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)

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).

Steps: 5

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.