Download App

STD 12 -7. Alternating current — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 12 -7. Alternating current4 Marks
Question
An $ac$ source of angular frequency $\omega$ is fed across a resistor r and a capacitor $C$ in series. The current registered is $I$. If now the frequency of source is changed to $\omega$ $/3$ (but maintaining the same voltage), the current in then circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$
✓

Answer

(a) At angular frequency $\Omega$, the current in $RC$ circuit is given by

${i_{rms}} = \frac{{{V_{rms}}}}{{\sqrt {{R^2} + {{\left( {\frac{1}{{\omega C}}} \right)}^2}} }}$                                                ......$(i)$

Also $\frac{{{i_{rms}}}}{2} = \frac{{{V_{rms}}}}{{\sqrt {{R^2} + {{\left( {\frac{1}{{\frac{\omega }{3}C}}} \right)}^2}} }} = \frac{{{V_{rms}}}}{{\sqrt {{R^2} + \frac{9}{{{\omega ^2}{C^2}}}} }}$                 ......$(ii)$

From equation $(i)$ and $(ii)$ we get

$3{R^2} = \frac{5}{{{\omega ^2}{C^2}}} \Rightarrow \frac{{\frac{1}{{\omega C}}}}{R} = \sqrt {\frac{3}{5}} $==> $\frac{{{X_C}}}{R} = \sqrt {\frac{3}{5}} $

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

The volume of a gas at pressure $21 \times {10^4}\,N/{m^2}$ and temperature $27^o C$ is $83 $ litres. If $R = 8.3\ J/mol/K$, then the quantity of gas in $gm-mole$ will be
→
Two inductors $L_1$ (inductance $1 \mathrm{mH}$, internal resistance $3 \Omega$ ) and $L_2$ (inductance $2 \mathrm{mH}$, internal resistance $4 \Omega$ ), and a resistor $R$ (resistance $12 \Omega$ ) are all connected in parallel across a $5 \mathrm{~V}$ battery. The circuit is switched on at time $t=0$. The ratio of the maximum to the minimum current $\left(I_{\max } / I_{\min }\right)$ drawn from the battery is
→
A car travels a distance $S$ on a straight road in two hours and then returns to the starting point in the next three hours. Its average velocity is
→
In the figure, a ball of mass $m$ is tied with two strings of equal length as shown. If the rod is rotated with angular velocity $\omega$, then
→
Benzaldehyde $ + NaOH \to $
→
In the arrangement shown in figure the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $ U$. Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed
→
An ideal gas filled in a cylinder occupies volume $V$. The gas is compressed isothermally to the volume $V/3$. Now, the cylinder valve is opened and the gas is allowed to leak keeping temperature same. What percentage of the number of molecules should escape to bring the pressure in the cylinder back to its original value?
→
$\sqrt{d_{1}}$ and $\sqrt{d_{2}}$ are the impact parameters corresponding to scattering angles $60^{\circ}$ and $90^{\circ}$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For $d_{1}=x d_{2}$, the value of $x$ will be ________
→
Assertion : The ferromagnetic substance do not obey Curie’s law.

Reason : At Curie point a ferromagnetic substance start behaving as a paramagnetic substance.

→
A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

$F=F_{0}\left(1-\left(\frac{t-T}{T}\right)^{2}\right)$

Where $F_{0}$ and $T$ are constants. The force acts only for the time internal $2 T$. The velocity $v$ of the particle after time $2 {T}$ is -

→