In the shown AC circuit phase different between currents I_1 and … - Vidyadip

MCQ

In the shown $AC$ circuit phase different between currents $I_1$ and $I_2$ is

A
$\frac{\pi }{2} - {\tan ^{ - 1}}\,\frac{{{x_L}}}{R}$
B
${\tan ^{ - 1}}\,\frac{{{x_L} - {x_C}}}{R}$
✓
$\frac{\pi }{2} + {\tan ^{ - 1}}\,\frac{{{x_L}}}{R}$
D
${\tan ^{ - 1}}\,\frac{{{x_L} - {x_C}}}{R} + \frac{\pi }{2}$

✓

Answer

Correct option: C.

$\frac{\pi }{2} + {\tan ^{ - 1}}\,\frac{{{x_L}}}{R}$

c
Current leads the voltage by $\frac{\pi}{2}$ in capacitor and by $\frac{\tan ^{-1} X_{L}}{R}$ in $R L$ circuit phase difference in $I_{1}$ and $I_{2}$

$=\frac{\pi}{2}+\frac{\tan ^{-1} X_{L}}{R}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A light whose electric field vectors are completely removed by using a good Polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

Three masses are placed on the $x-$axis $: 300\, g$ at origin, $500 \,g$ at $x = 40\, cm$ and $400\, g$ at $x = 70\, cm.$ The distance of the centre of mass from the origin is ....... $cm$

A bimetallic strip is formed out of two identical strips, one of copper and other of brass. The coefficients of linear expansion of the two metals are ${\alpha _C}$ and ${\alpha _{B}}.$ On heating, the temperature of the strip goes up by $\Delta T$ and the strip bends to form an arc of radius of curvature $R.$ Then $R$ is

In an series $A.C.$ circuit the current and voltage are given respectively as

$I = 10\,\sin \,\omega t$ ; $V = 10\,\sin \,\left( {\omega t + \pi /4} \right)$

then which of the following element may be present in the circuit
$(a)$ Only $C$ $(b)$ All $L, C$ and $R$ $(c)$ Both $C$ and $R$ $(d)$ Both $L$ and $R$

A current carrying loop is placed in a uniform magnetic field. The torque acting on it does not depend upon

A particle of mass $250\,g$ executes a simple harmonic motion under a periodic force $F =(-25\,x) N$. The particle attains a maximum speed of $4\,m / s$ during its oscillation. The amplitude of the motion is $...........cm$.

A ball is dropped from a height of $20 \ m$ above the surface of water in a lake. The refractive index of water is $4/3$. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8\ m$ above the water surface the fish sees the speed of ball as........$m/s$ $[ g = 10\ m/s^2.]$

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is:

Molybdenum is used as a target element for production of $X-$ rays because it is

Initially system is in equilibrium. Time period of $SHM$ of block in vertical direction is