JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
In an \(LCR \) circuit as shown below both switches are open initially. Now switch \(S_1\) is closed, \(S_2\) kept open. ( \(q\) is charge on the capacitor and \(\tau = RC\) is Capacitive time constant). Which of the following statement is correct?
- A At \(t=\frac{\tau}{2}\),\(q=C V\) \((1-e^{-1})\)
- B Work done by the battery is half of the energy dissipated in the resistor
- C At \(t=\)\(\;\tau \) ,\(q= \) \(\frac{{{\rm{CV}}}}{2}\)
- D At \(t= \)\({2 \tau }\) ,\(q=CV\) \((1-e^{-2})\)
Answer & Solution
Correct Answer
(D) At \(t= \)\({2 \tau }\) ,\(q=CV\) \((1-e^{-2})\)
Step-by-step Solution
Detailed explanation
Charge on he capacitor at any time \(t\) is given by \(q=C V\left(1-e^{t / \tau}\right)\) at \(t=2 \tau\) \(q=C V\left(1-e^{-2}\right)\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant \(K\) is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \(\frac{3}{4} d\), where \('d'\) is the separation between the plates of parallel plate capacitor. The new capacitance \((C')\) in terms of original capacitance \(\left( C _{0}\right)\) is given by the following relationJEE Mains 2021 Medium
- Two light identical springs of spring constant \(k\) are attached horizontally at the two ends of a uniform horizontal rod \(AB\) of length \(l\) and mass \(m\). the rod is pivoted at its centre \(‘O’\) and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is
JEE Mains 2019 Hard - The binding energy for the following nuclear reactions are expressed in MeV .
\({ }_2 He ^3+{ }_0 n ^1 \rightarrow{ }_2 He ^4+20 MeV\)
\({ }_2 He ^4+{ }_0 n ^1 \rightarrow{ }_2 He ^5-0.9 MeV\)
If \(X _3, X _4, X _5\) denote the stability of \({ }_2 He ^3,{ }_2 He ^4\) and \({ }_2 He ^5\), respectively, then the correct order is :JEE Mains 2026 Medium - Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is \(5.0 \mathrm{~cm}\). The magnitude of the magnetic field at a point \(P\) midway between the wires is __________\(\mu \mathrm{T}\) (Given : \(\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\) )
JEE Mains 2024 Hard - The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )JEE Mains 2026 Easy - Speed of a transverse wave on a straight wire (mass \(6.0\; \mathrm{g}\), length \(60\; \mathrm{cm}\) and area of cross-section \(1.0\; \mathrm{mm}^{2}\) ) is \(90\; \mathrm{ms}^{-1} .\) If the Young's modulus of wire is \(16 \times 10^{11}\; \mathrm{Nm}^{-2},\) the extension of wire over its natural length isJEE Mains 2020 Easy
More PYQs from JEE Mains
- The pair of physical quantities not having same dimensions is :JEE Mains 2025 Easy
- A beam of plane polarised light of large cross sectional area and uniform intensity of \(3.3 \,Wm ^{-2}\) falls normally on a polariser (cross sectional area \(3 \times 10^{-4}\, m ^{2}\) ) which rotates about its axis with an angular speed of \(31.4\, rad/s.\) The energy of light passing through the polariser per revolution, is close to ........ \( \times 10^{-4} \,J\)JEE Mains 2020 Hard
- A beam of light has two wavelengths of \(4972\,\mathop A\limits^o \) and \(6216\,\mathop A\limits^o \) with a total intensity of \(3 .6 \times 10^{- 3}\,\,Wm^{-2}\) equally distributed among the two wavelengths. The beam falls normally on an area of \(1\,cm^2\) of a clean metallic surface of work function \( 2.3\,eV.\) Assume that there is no loss of light by reflection and that each capable photon ejects one electron. The number of photoelectrons liberated in \(2\,s\) is approximatelyJEE Mains 2014 Hard
- The the circle passing through the foci of the \(\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1\) and having centre at \((0,3) \) isJEE Mains 2013 Medium
- The number of distinct real roots of the equation \(3 x^{4}+4 x^{3}-12 x^{2}+4=0\) is ..... .JEE Mains 2021 Hard
- Let \(\mathrm{Q}\) and \(\mathrm{R}\) be the feet of perpendiculars from the point \(\mathrm{P}(\mathrm{a}, \mathrm{a}, \mathrm{a})\) on the lines \(\mathrm{x}=\mathrm{y}, \mathrm{z}=1\) and \(\mathrm{x}=-\mathrm{y}\), \(\mathrm{z}=-1\) respectively. If \(\angle \mathrm{QPR}\) is a right angle, then \(12 \mathrm{a}^2\) is equal toJEE Mains 2024 Hard