Question

In $\mathrm{R}-\mathrm{L}$ circuit, the time lag between the voltage maximum and current maximum is:
(A) $\omega \phi$
(B) $\mathrm{L} / \mathrm{R}$
(C) $\omega / \phi$
(D) $\mathrm{R} / \mathrm{L}$

Answer 1

Hint: We know that the natural response of an RL circuit describes the inductor current in a circuit consisting only of resistors and a single equivalent inductance. The circuit is source-free; the response is entirely due to energy initially stored in the inductor. A source-free circuit is where all independent sources have been disconnected from the circuit after some switch action. The voltages and currents in the circuit typically will have some transient response due to initial conditions (initial capacitor voltages and initial inductor currents).

Complete step by step answer
We know that a circuit that contains a pure resistance R ohm connected in series with a coil having a pure inductance of L (Henry) is known as RL Series Circuit. When an AC supply voltage V is applied, the current flows in the circuit. A LR Series Circuit consists basically of an inductor of inductance, L connected in series with a resistor of resistance, R. The resistance “R” is the DC resistive value of the wire turns or loops that goes into making up the inductors coil.
In a R-L the current lags behind the voltage by
$\tan ^{-1}\left\{\dfrac{\mathrm{L}}{\mathrm{R}}\right\}$ radians.
Also let "t " be the time by which the current lags behind the
voltage.
Then we can say that:
$\omega \mathrm{t}=\tan ^{-1} \dfrac{\mathrm{L}}{\mathrm{R}}$
So now we can write that:
$\mathrm{t}=\dfrac{1}{\omega} \tan ^{-1} \dfrac{\mathrm{L}}{\mathrm{R}}$
Therefore, the time "t", by which current lags behind the voltage is proportional to $\dfrac{\mathrm{L}}{\mathrm{R}}$

So, option B is correct.

Note: For our knowledge we know that the RC circuit is a series connection of resistance and capacitance, this circuit stores energy in the form of electric field. The RL circuit is a series combination of resistance and inductance which stores energy in the form of magnetic energy. The RC circuit is used in camera flashes, pacemaker, timing circuit etc. The forced response is what the circuit does with the sources turned on, but with the initial conditions set to zero. The natural response is what the circuit does including the initial conditions, but with the input suppressed. The RC circuit is used in camera flashes, pacemaker, timing circuit etc. The RC signal filters the signals by blocking some frequencies and allowing others to pass through it. It is also called first-order RC circuit and is used to filter the signals bypassing some frequencies and blocking others.