MCQ
A sinusoidal voltage of peak value $283\, V$ and angular frequency $320/s$ is applied to a series $LCR$ circuit. Given that $R\, = 5\,\Omega $ , $L\,= 25\, mH$ and $C\, = 1000\, \mu F$. The total impedance, and phase difference between the voltage across the source and the current will respectively be
  • A
    $10\,\Omega \,\,$ and $\,\,\,{\tan ^{ - 1}}\left( {\frac{5}{3}} \right)$
  • $7\,\Omega \,\,$ and $45^o$
  • C
    $10\,\Omega \,\,$ and $\,\,\,{\tan ^{ - 1}}\left( {\frac{8}{3}} \right)$
  • D
    $7\,\Omega \,\,$ and $\,\,\,{\tan ^{ - 1}}\left( {\frac{5}{3}} \right)$

Answer

Correct option: B.
$7\,\Omega \,\,$ and $45^o$
b
Given,

$\mathrm{V}_{0}=283 \,\mathrm{volt}, \omega=320,\, \mathrm{R}=5 \,\Omega, \mathrm{L}=25 \,\mathrm{mH}, \mathrm{C} =1000 \,\mu \mathrm{F}$

$x_{L}=\omega L=320 \times 25 \times 10^{-3}=8\, \Omega$

$x_{C}=\frac{1}{\omega C}=\frac{1}{320 \times 1000 \times 10^{-6}}=3.1 \,\Omega$

Total impedance of the circuit:

$z=\sqrt{\mathrm{R}^{2}+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^{2}}=\sqrt{25+(4.9)^{2}}=7\, \Omega$

Phase difference between the voltage and current

$\tan \phi=\frac{\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}}{\mathrm{R}}$

$\tan \phi=\frac{4.9}{5} \approx 1 \Rightarrow \phi=45 \%$

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

Similar questions

In a Young's double slit experiment, the separation between the slits is $0.15\; \mathrm{mm}$. In the experiment, a source of light of wavelength $589 \;\mathrm{nm}$ is used and the interference pattern is observed on a screen kept $1.5\; \mathrm{m}$ away. The separation between the successive bright fringes on the screen is......$mm$
A vertical straight conductor carries a current vertically upwards. A point P lies to the east of it at a small distance and another point Q lies to the west at the same distance. The magnetic field at P is
The amount of substance liberated on electrodes during electrolysis when 1 coulomb of electricity is passed, is
A particle is fastened at the end of a string and is whirled in a vertical circle with the other end of the string being fixed. The motion of the particle is:
Assume that an electric field $\vec E = 30{x^2}\hat i$ exists in space. Then the potential difference $V_A-V_O$ where $V_O$ is the potential at the origin and $V_A$ the potential at $x = 2\ m$ is....$V$
A hollow tube is carrying an electric current along its length distributed uniformly over its surface. The magnetic field:
A 10 micro-farad capacitor is charged to 500 V and then its plates are joined together through a resistance of 10 ohm. The heat produced in the resistance is
Find the number of electrons emitted per second by a $24 \,W$ source of monochromatic light of wavelength $6600 \mathring A$, assuming $3 \%$ efficiency for photoelectric effect (take $h=6.6 \times 10^{-34} \,Js$ ) $S$
A person can see clearly objects only when they lie between $50\,\, cm$ and $400\,\, cm$ from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be
Light of wavelength $589.3\,nm$ is incident normally on the slit of width $0.1\,mm.$ What will be the angular width of the central diffraction maximum at a distance of $1\,m$ from the slit........$^o$