If $C$ and $L$ denote the capacitance and inductance, the dimensions of $L C$ are

[M^{0} L^{0} T^{- 1}]

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[M^{0} L^{- 1} T^{0}]

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[M^{- 1} L^{- 1} T^{0}]

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[M^{0} L^{0} T^{2}]

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Solution

The correct option is D $[M^{0} L^{0} T^{2}]$
The frequency $v$ of a circuit consisting of capacitance and inductance is given as $v = \frac{1}{2 π \sqrt{L C}}$
So, $[L C] = \frac{1}{(2 π v)^{2}} = \frac{1}{(T^{- 1})^{2}} = [T^{2}] = [M^{0} L^{0} T^{2}]$

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Q. Find the dimensions of

\frac{1}{\sqrt{L C}}

(L = Inductance, C = Capacitance).

Q. If

C

denotes the capacity and

L

denotes the inductance, the dimensions of '

L C

' are :

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If C and L denote the capacitance and inductance, the dimensions of LC are

The correct option is D [M0L0T2]The frequency v of a circuit consisting of capacitance and inductance is given as v=12π√LCSo, [LC]=1(2πv)2=1(T−1)2=[T2]=[M0L0T2]

If $C$ and $L$ denote the capacitance and inductance, the dimensions of $L C$ are

The correct option is D $[M^{0} L^{0} T^{2}]$
The frequency $v$ of a circuit consisting of capacitance and inductance is given as $v = \frac{1}{2 π \sqrt{L C}}$
So, $[L C] = \frac{1}{(2 π v)^{2}} = \frac{1}{(T^{- 1})^{2}} = [T^{2}] = [M^{0} L^{0} T^{2}]$