If C, R, L and I denote capacity,resistance,i | vedclass

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

Question

(D) The dimensional formulas are:$[C] = [M^{-1} L^{-2} T^4 A^2]$$[R] = [M L^2 T^{-3} A^{-2}]$$[L] = [M L^2 T^{-2} A^{-2}]$$[I] = [A]$$(1)$ $[CR] = [M^

Vedclass · Accepted Answer

$(1)$,$(2)$ and $(3)$ only

Vedclass · Answer

(D) The dimensional formulas are:$[C] = [M^{-1} L^{-2} T^4 A^2]$$[R] = [M L^2 T^{-3} A^{-2}]$$[L] = [M L^2 T^{-2} A^{-2}]$$[I] = [A]$$(1)$ $[CR] = [M^{-1} L^{-2} T^4 A^2] 	imes [M L^2 T^{-3} A^{-2}] = [T^1]$. This represents time.$(2)$ $[L/R] = [M L^2 T^{-2} A^{-2}] / [M L^2 T^{-3} A^{-2}] = [T^1]$. This represents time.$(3)$ $[\sqrt{LC}] = ([M L^2 T^{-2} A^{-2}] 	imes [M^{-1} L^{-2} T^4 A^2])^{1/2} = [T^2]^{1/2} = [T^1]$. This represents time.$(4)$ $[LI^2] = [M L^2 T^{-2} A^{-2}] 	imes [A^2] = [M L^2 T^{-2}]$. This represents energy,not time.Thus,quantities $(1)$,$(2)$,and $(3)$ have the dimensions of time. Therefore,option $(d)$ is correct.

If $C, R, L$ and $I$ denote capacity,resistance,inductance and electric current respectively,the quantities having the same dimensions of time are :
$(1)$ $C R$
$(2)$ $\frac{L}{R}$
$(3)$ $\sqrt{L C}$
$(4)$ $L I^2$

Similar Questions

$A$ choke coil is preferred to a $Rheostat$ in $AC$ circuits because:

$A$ direct current of $10 \,A$ is superimposed on an alternating current $I = 40 \cos \omega t \; (A)$ flowing through a wire. The effective value of the resulting current will be ....... $A$.

$A$ $\frac{2.5}{\pi} \mu F$ capacitor and $3000 \, \Omega$ resistor are joined in series to an $AC$ source of $200 \, V$ and $50 \, Hz$ frequency. The power factor of the circuit and the power dissipated in it will respectively be:

In the given $AC$ circuit,when switch $S$ is at position $1$,the source $emf$ leads the current by $\pi / 6$. Now,if the switch is at position $2$,then

In an $A.C.$ circuit,the instantaneous $e.m.f.$ and current are given by:
$e = 100 \sin(20t)$
$i = 20 \sin(30t - \frac{\pi}{4})$
In one cycle of $A.C.$,the average power consumed by the circuit and the wattless current are,respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

If $C, R, L$ and $I$ denote capacity,resistance,inductance and electric current respectively,the quantities having the same dimensions of time are :$(1)$ $C R$$(2)$ $\frac{L}{R}$$(3)$ $\sqrt{L C}$$(4)$ $L I^2$