L, C, R represent physical quantities inducta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The dimensions of $L$ are $[M L^2 T^{-2} A^{-2}]$.The dimensions of $C$ are $[M^{-1} L^{-2} T^4 A^2]$.The dimensions of $R$ are $[M L^2 T^{-3} A^{

Vedclass · Accepted Answer

$1/\sqrt{LC}$

Vedclass · Answer

(C) The dimensions of $L$ are $[M L^2 T^{-2} A^{-2}]$.The dimensions of $C$ are $[M^{-1} L^{-2} T^4 A^2]$.The dimensions of $R$ are $[M L^2 T^{-3} A^{-2}]$.For the combination $1/\sqrt{LC}$:$\frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{[M L^2 T^{-2} A^{-2}] 	imes [M^{-1} L^{-2} T^4 A^2]}} = \frac{1}{\sqrt{T^2}} = T^{-1}$.Since $T^{-1}$ is the dimension of frequency,option $C$ is correct.Note: $R/L$ also has dimensions of frequency $(T^{-1})$,but $1/\sqrt{LC}$ is the standard resonant frequency combination.

$L, C, R$ represent physical quantities inductance,capacitance,and resistance respectively. The combinations which have the dimensions of frequency are

Similar Questions

The $Q$ factor of a series $\text{LCR}$ circuit with $L=2 \text{ H}$,$C=32 \mu\text{F}$ and $R=10 \Omega$ is :-

The current in a series $LCR$ circuit will be maximum when $\omega$ is

In the circuit shown,the power factor of the circuit is $1$ and the power factor of the box is $\frac{3}{5}$. Find the reading of the ammeter in $A$.

The $Q$-value of a series $LCR$ circuit with $L=2 \ H$,$C=32 \ \mu F$,and $R=20 \ \Omega$ is:

In a series resonant $L-C-R$ circuit,the voltage across $R$ is $100 \, V$ and $R = 1 \, k\Omega$ with $C = 2 \, \mu F$. The resonant frequency $\omega$ is $200 \, rad \, s^{-1}$. At resonance,the voltage across $L$ is.....$V$

Vedclass Test Series

Exam Paper Generator

Online Exam Module