In an AC circuit, if the voltage is given by V(t) = V_0 sin(ωt), what is the exp
Practice Questions
Q1
In an AC circuit, if the voltage is given by V(t) = V_0 sin(ωt), what is the expression for the current if the circuit is purely inductive? (2023)
I(t) = I_0 sin(ωt)
I(t) = I_0 sin(ωt - π/2)
I(t) = I_0 cos(ωt)
I(t) = I_0 cos(ωt + π/2)
Questions & Step-by-Step Solutions
In an AC circuit, if the voltage is given by V(t) = V_0 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) = V_0 sin(ωt), where V_0 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) = I_0 sin(ωt - π/2), where I_0 is the maximum current.
