When an ac source of e.m.f. e = E_0 (100 ,t) is connected across … - Vidyadip

Question

When an ac source of $e.m.f$. $e = {E_0}$$\sin (100\,t)$ is connected across a circuit, the phase difference between the $e.m.f$. $e$ and the current $i$ in the circuit is observed to be $\pi /4$, as shown in the diagram. If the circuit consists possibly only of $RC$ or $LC$ in series, find the relationship between the two elements

✓

Answer

(a) As the current i leads the voltage by $\frac{\pi }{4},$ it is an $RC$ circuit, hence $\tan \phi = \frac{{{X_C}}}{R}$==> $\tan \frac{\pi }{4} = \frac{1}{{\omega \,CR}}$
==> $\omega \,CR = 1$ as $\omega$ $= 100 \,rad/sec$
==> $CR = \frac{1}{{100}}se{c^{ - 1}}$.
From all the given options only option $(a)$ is correct.

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

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

Similar questions

A thermodynamic process is shown in the figure. The pressures and volumes corresponding to some points in the figure are :

${P_A} = 3 \times {10^4}Pa,\;{P_B} = 8 \times {10^4}Pa$ and ${V_A} = 2 \times {10^{ - 3}}{m^3},\;{V_D} = 5 \times {10^{ - 3}}{m^3}$

In process $AB$, $600 J$ of heat is added to the system and in process $BC, 200 J $ of heat is added to the system. The change in internal energy of the system in process $ AC$ would be ...... $J$

$A$ block of mass $m$ is kept in an elevation which starts moving downward with an acceleration $a$ as shown in figure. The block is observed by two observers $A$ and $B$ for a time interval $t_0$. The observer $B$ finds that the work done by pseudo force on the block is

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If $r_{d}$ and $r_{p}$ are the radii of their circular paths respectively, then the ratio $\frac{r_{d}}{r_{p}}$ will be $\sqrt{ x }: 1$ where $x$ is ..........

In a radio receiver, the short wave and medium wave stations are tuned by using the same capacitor but coils of different inductance $L_s$ and $L_m$ respectively then

Which arrangement of four identical resistances should be used to draw maximum energy from a cell of voltage $V$

A $10 \,m$ long potentiometer wire is connected to a battery having a steady voltage. A Leclanche cell is balanced at $4 \,m$ length of the wire. If the length is kept the same, but its cross-section is doubled, the null point will be obtained at ........... $m$

The angular momentum of an electron in the $2^{nd}$ excited state of a Helium ion $(He^+)$ is

Stress to strain ratio is equivalent to

A Car not engine whose low temperate reservoir is at $7\,^oC$ has an efficiency of $50\%$ . It is desired to increase the efficiency to $70\%$ . By how many degrees should the temperature of the high temperature reservoir be increased .... $K$

An infinite sequence of resistance is shown in the figure. The resultant resistance between $A$ and $B$ will be, when ${R_1} = 1\,ohm$ and ${R_2} = 2\,ohm$ ............. $\Omega$