JEE PYQ: Units And Dimensions Question 11
Question 11 - 2020 (05 Sep Shift 2)
The quantities $x = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$, $y = \frac{E}{B}$ and $z = \frac{1}{CR}$ are defined where $C$-capacitance, $R$-resistance, $l$-length, $E$-electric field, $B$-magnetic field and $\varepsilon_0$, $\mu_0$ - free space permittivity and permeability respectively. Then:
(1) $x$, $y$ and $z$ have the same dimension.
(2) Only $x$ and $z$ have the same dimension.
(3) Only $x$ and $y$ have the same dimension.
(4) Only $y$ and $z$ have the same dimension.
Show Answer
Answer: (1)
Solution
Speed of light $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} = x$. Also $\frac{E}{B} = c = y$. Time constant $\tau = RC = t$, so $z = \frac{1}{RC} = \frac{l}{t} =$ Speed. Thus $x$, $y$, $z$ all have the same dimension of speed.
BETA
