Question

An inductor and resistor are connected in series with an ac source. In this circuit.

• A. The current and the PD across the resistance lead the PD across the inductance
• B. The current and the PD across the resistance lag behind the PD across the inductance by an angle $\pi /2$
• C. The current and the PD across the resistance lag behind the PD across the inductance by an angle $\pi$
• D. The PD across the resistance lags behind the PD across the inductance by an angle $\pi /2$ but the current in resistance leads the PD across the inductance by $\pi /2$

Answer 1

The correct option is B The current and the PD across the resistance lag behind the PD across the inductance by an angle $\pi /2$

In phasor, source voltage = $V$
Impedance = $R+jL\omega =\left|Z\right|\angle \theta$
$\theta =ta{n}^{-1}L\omega /R$
$I=\frac{V}{\left|Z\right|}\angle -\theta$
Voltage across $R=IR=\frac{VR}{\left|Z\right|}\angle -\theta$
Voltage across inductor = $IjL\omega =jL\omega \frac{V}{\left|Z\right|}\angle (-\theta )=\frac{VL\omega }{\left|Z\right|}\angle (-\theta +90)$