Question

The response of a 1-$\phi$ R-L series circuit is \( i(t) = Ae^{-\frac{R}{L}t} + I_m \sin(\omega t - \theta) \). Then the supply voltage should be:

• A. \( V_m \sin(\omega t + \varphi) \)
• B. \( V_m \sin(\omega t - \varphi) \)
• C. \( V_m \sin(\omega t) \)
• D. \( V_m \sin(\omega t) + \text{Exponential source} \)

Hint:

In R-L circuits, voltage always leads current; in R-C circuits, current leads voltage.

Answer 1

The Correct Option is A

In an R-L series circuit with sinusoidal steady state response: - Supply voltage leads the current by a phase angle \( \varphi \) Thus: \[ v(t) = V_m \sin(\omega t + \varphi) \]