- Home
- Standard 11
- Physics
1.Units, Dimensions and Measurement
medium
Match List$-I$ with List$-II.$
| List$-I$ | List$-II$ |
| $(a)$ Capacitance, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
| $(b)$ Permittivity of free space, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
| $(c)$ Permeability of free space, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
| $(d)$ Electric field, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
A$(a) \rightarrow(i i i),(b) \rightarrow(i i),(c) \rightarrow(i v),(d) \rightarrow(i)$
B$(a) \rightarrow(i i i),(b) \rightarrow(i v),(c) \rightarrow(i i),(d) \rightarrow(i)$
C$(a) \rightarrow(iv),(b) \rightarrow(i i),(c) \rightarrow(iii),(d) \rightarrow(i)$
D$(a) \rightarrow(iv),(b) \rightarrow(iii),(c) \rightarrow(ii),(d) \rightarrow(i)$
(JEE MAIN-2021)
Solution
As we know
$q=C V$
${[C]=\left[\frac{q}{V}\right]=\frac{(A \times T)^{2}}{M L^{2} T^{-2}}}$
$=M^{-1} L^{-2} T^{4} A^{2}$
${[E]=\left[\frac{F}{q}\right]=\frac{M L T^{-2}}{A T}}$
$=M L T_{q}^{-3} A^{-1}$
$F=\frac{q_{1} q_{2}}{4 \pi \epsilon_{0} r^{2}}$
${\left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{4} A^{2}}$
$\text { Speed of light } c=\frac{1}{\sqrt{\mu_{0} \in_{0}}}$
$\mu_{0}=\frac{1}{\epsilon_{0} c^{2}}$
${\left[\mu_{0}\right]=\frac{1}{\left[M^{-1} L^{-3} T^{4} A^{2}\right]\left[L T^{-1}\right]^{2}}}$
$=\left[M^{1} L^{1} T^{-2} A^{-2}\right]$
$q=C V$
${[C]=\left[\frac{q}{V}\right]=\frac{(A \times T)^{2}}{M L^{2} T^{-2}}}$
$=M^{-1} L^{-2} T^{4} A^{2}$
${[E]=\left[\frac{F}{q}\right]=\frac{M L T^{-2}}{A T}}$
$=M L T_{q}^{-3} A^{-1}$
$F=\frac{q_{1} q_{2}}{4 \pi \epsilon_{0} r^{2}}$
${\left[\epsilon_{0}\right]=M^{-1} L^{-3} T^{4} A^{2}}$
$\text { Speed of light } c=\frac{1}{\sqrt{\mu_{0} \in_{0}}}$
$\mu_{0}=\frac{1}{\epsilon_{0} c^{2}}$
${\left[\mu_{0}\right]=\frac{1}{\left[M^{-1} L^{-3} T^{4} A^{2}\right]\left[L T^{-1}\right]^{2}}}$
$=\left[M^{1} L^{1} T^{-2} A^{-2}\right]$
Standard 11
Physics
