Quantum hall resistance R_H is a fundamental constant with dimensions of resistance. If h is Planck&

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

hard

The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as

$\frac{e^2}{h}$

$\frac{h}{e^2}$

$\frac{h^2}{e}$

$\frac{e}{h^2}$

(KVPY-2011)

Solution

(b)

Let $R_H=k h^a e^b \quad \dots(i)$

As, $R=\frac{V}{I}$

$\therefore {\left[R_H\right] } =\left[ ML ^2 T ^{-3} A ^{-2}\right]$

$\Rightarrow h =E \cdot t$

$\Rightarrow {[h] }=\left[ ML ^2 T ^{-1}\right]$

$e=I \cdot t \Rightarrow[e]=[ A \cdot T ]$

Substituting above values in Eq. $(i)$, we have

${\left[ ML ^2 T ^{-3} A ^{-2}\right] }=k\left[ ML ^2 T ^{-1}\right]^e[ AT ]^b$

$=k\left[ M ^a L ^{2 a} T ^{-a+b} A ^b\right]$

Equating dimensions, we get

$a=1 \text { and } b=-2$

Hence, $\quad R_H=k\left(\frac{h}{e^2}\right)$

So, dimensions of hall resistance are same as that of $\frac{h}{e^2}$.

Standard 11

Physics

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

hard

(JEE MAIN-2017)

The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be

hard

(AIIMS-2008)

A function $f(\theta )$ is defined as $f(\theta )\, = \,1\, – \theta + \frac{{{\theta ^2}}}{{2!}} – \frac{{{\theta ^3}}}{{3!}} + \frac{{{\theta ^4}}}{{4!}} + …$ Why is it necessary for $f(\theta )$ to be a dimensionless quantity ?

hard

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\, sin\, ct + b\, cos\, dx$, then the dimension of $a/b$ is

easy

Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

hard

(JEE MAIN-2024)

The quantum hall resistance $R_H$ is a fundamental constant with dimensions of resistance. If $h$ is Planck's constant and $e$ is the electron charge, then the dimension of $R_H$ is the same as

Solution

Similar Questions

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

The speed of light $(c)$, gravitational constant $(G)$ and planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be

A function $f(\theta )$ is defined as $f(\theta )\, = \,1\, – \theta + \frac{{{\theta ^2}}}{{2!}} – \frac{{{\theta ^3}}}{{3!}} + \frac{{{\theta ^4}}}{{4!}} + …$ Why is it necessary for $f(\theta )$ to be a dimensionless quantity ?

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a\, sin\, ct + b\, cos\, dx$, then the dimension of $a/b$ is

Applying the principle of homogeneity of dimensions, determine which one is correct. where $\mathrm{T}$ is time period, $\mathrm{G}$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

Start a Free Trial Now