If L,C,and R denote the inductance,capacitanc | vedclass

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

Question

(B) We know that the resonant frequency of an $LC$ circuit is given by $f = \frac{1}{2\pi \sqrt{LC}}$.Therefore,the dimensions of $LC$ are $[LC] = [T^

Vedclass · Accepted Answer

$[M^{0}L^{0}T^{3}I^{0}]$

Vedclass · Answer

(B) We know that the resonant frequency of an $LC$ circuit is given by $f = \frac{1}{2\pi \sqrt{LC}}$.Therefore,the dimensions of $LC$ are $[LC] = [T^{2}]$.Also,the time constant of an $LR$ circuit is $	au = \frac{L}{R}$,so the dimensions of $\frac{L}{R}$ are $[T]$.This implies that the dimensions of $\frac{R}{L}$ are $[T^{-1}]$.Now,we need to find the dimensions of $C^{2}LR$.We can rewrite the expression as $C^{2}LR = (LC) \cdot (RC)$.Since $RC$ is the time constant of an $RC$ circuit,its dimensions are $[T]$.Thus,$[C^{2}LR] = [LC] \cdot [RC] = [T^{2}] \cdot [T] = [T^{3}]$.Alternatively,$[C^{2}LR] = [LC] \cdot [LC] \cdot [R/L] = [T^{2}] \cdot [T^{2}] \cdot [T^{-1}] = [T^{3}]$.Therefore,the dimensional formula is $[M^{0}L^{0}T^{3}I^{0}]$.

If $L$,$C$,and $R$ denote the inductance,capacitance,and resistance respectively,the dimensional formula for $C^{2}LR$ is

Similar Questions

If the dimensions of length are expressed as ${G^x}{c^y}{h^z}$; where $G, c$ and $h$ are the universal gravitational constant,speed of light,and Planck's constant respectively,then:

In a system of units,if force $(F)$,acceleration $(A)$,and time $(T)$ are taken as fundamental units,then the dimensional formula of energy is:

Planck's constant $(h)$,speed of light in vacuum $(c)$,and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length?

In the equation,pressure $P = \frac{c - t^{2}}{DS}$,where $S$ and $t$ represent the distance and time respectively. The dimensions of $\left(\frac{D}{c}\right)$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module