JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
If the capacitance of a nanocapacitor is measured in terms of a unit \(u\) made by combining the electric charge \(e,\) Bohr radius \(a_0,\) Planck's constant \(h\) and speed of light \(c\) then
- A \(u\, = \,\frac{{{e^2}h}}{{{a_0}}}\)
- B \(u\, = \,\frac{{hc}}{{{e^2}{a_0}}}\)
- C \(u\, = \,\frac{{{e^2}c}}{{h{a_0}}}\)
- D \(u\, = \,\frac{{{e^2}{a_0}}}{{hc}}\)
Answer & Solution
Correct Answer
(D) \(u\, = \,\frac{{{e^2}{a_0}}}{{hc}}\)
Step-by-step Solution
Detailed explanation
The unit of capacitance is \(\frac {Coulomb}{V} = \frac {Coulomb}{\text{work done per unit charge}}\)=\(\frac{\text { Coulomb }}{\frac{ W }{\text { Coulomb }}}=\frac{\text { Coulomb }^{2}}{ kgm ^{2} s ^{-2}}= C ^{2} kg ^{-1} m ^{-2} s ^{2}\) Checking units of each option:…
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
- The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of \(3 rd\) orbit will be \(.........R\)JEE Mains 2023 Easy
- The acceleration of an electron in the first orbit of the hydrogen atom \((z\, = 1)\) isJEE Mains 2017 Hard
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio \(3: 2\). The ratio of their nuclear sizes will be \(\left(\frac{x}{3}\right)^{\frac{1}{3}}\). The value of ' \(x\) ' is :JEE Mains 2023 Medium
- The current \(I_{1}\) (in \(A\)) flowing through \(1\; \Omega\) resistor in the following circuit is:
JEE Mains 2020 Medium - An electric bulb rated as \(100 \mathrm{~W}-220 \mathrm{~V}\) is connected to an ac source of rms voltage 220 V. The peak value of current through the bulb is :JEE Mains 2025 Easy
- The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M . Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its centre. The magnitudes of the acceleration experienced by the blocks is _________ (assume no slipping of string on pulley.)
JEE Mains 2026 Easy
More PYQs from JEE Mains
- A long straight wire of radius ' \(a\) ' carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at \(\frac{a}{2}\) and \(2\)a from axis of the wire is _______.JEE Mains 2024 Hard
- A block of mass \(0.1\, kg\) is connected to an elastic spring of spring constant \(640\, Nm^{-1}\) and oscillates in a damping medium of damping constant \(10^{-2}\, kg\,s^{-1}\) . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to ..... \(s\)JEE Mains 2017 Hard
- A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will beJEE Mains 2023 Medium
- The angle of elevation of the top of a vertical tower from a point \(P\) on the horizontal ground was observed to be \(\alpha \). After moving a distance \(2\, metres\) from \(P\) towards the foot of the tower, the angle of elevation changes to \(\beta \). Then the height (in metres) of the tower isJEE Mains 2014 Hard
- The critical angle of a medium for a specific wavelength, if the medium has relative permittivity \(3\) and relative permeability \(\frac{4}{3}\) for this wavelength, will be.....\(^o\)JEE Mains 2020 Medium
- A particle starts simple harmonic motion from the mean position. Its amplitude is \(a\) and total energy \(E\). At one instant its kinetic energy is \(3E/4.\) Its displacement at that instant isJEE Mains 2021 Medium