If C denotes the capacitance and L denotes the inductance, then the dimensional formula of L C is

Question

If C denotes the capacitance and L denotes the inductance, then the dimensional formula of L C is (A) [ M 0 L 0 T 2] (B) [ M 1 L 0 T 2] (C) [ M 1 L 1 T 2] (D) [ M 0 L 1 T 2]

Tardigrade Admin · Accepted Answer

Resonant frequency f=(1/√L C) ⇒ [L C]=[(1/f2)]=[ T 2]=[ M 0 L 0 T 2]

Q. If $C$ denotes the capacitance and $L$ denotes the inductance, then the dimensional formula of $L C$ is

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

$[M^{1} L^{0} T^{2}]$

$[M^{1} L^{1} T^{2}]$

$[M^{0} L^{1} T^{2}]$

Resonant frequency $f = \frac{1}{L C}$
$\Rightarrow [L C] = [\frac{1}{f ^{2}}] = [T^{2}] = [M^{0} L^{0} T^{2}]$

Q. If C denotes the capacitance and L denotes the inductance, then the dimensional formula of LC is

[M0L0T2]

[M1L0T2]

[M1L1T2]

[M0L1T2]