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1.Units, Dimensions and Measurement
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If $L , C$ and $R$ denote the inductance, capacitance and resistance respectively, the dimensional formula for $C ^{2} LR$ is
A$[M{L^{ - 2}}{T^{ - 1}}{I^0}]$
B$[{M^0}{L^0}{T^3}{I^0}]$
C$[{M^{ - 1}}{L^{ - 2}}{T^6}{I^2}]$
D$[{M^0}{L^0}{T^2}{I^0}]$
Solution
$[{C^2}LR]$ $= \left[ {{C^2}{L^2}\frac{R}{L}} \right]$ $=\left[ {{{(LC)}^2}\left( {\frac{R}{L}} \right)} \right]$
$f = \frac{1}{{2\pi }}\frac{1}{{\sqrt {LC} }}$
$LC = [{T^2}]\, \frac{L}{R} = [T]$. $\left[ {{{(LC)}^2}\left( {\frac{R}{L}} \right)} \right]\, $ $= \,{[{T^2}]^2}[{T^{ – 1}}] = [{T^3}]$ .
$f = \frac{1}{{2\pi }}\frac{1}{{\sqrt {LC} }}$
$LC = [{T^2}]\, \frac{L}{R} = [T]$. $\left[ {{{(LC)}^2}\left( {\frac{R}{L}} \right)} \right]\, $ $= \,{[{T^2}]^2}[{T^{ – 1}}] = [{T^3}]$ .
Standard 11
Physics
