Question

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

• A. (1) and (2) only
• B. (1) and (3) only
• C. (1) and (4) only
• D. (1),(2) and (3) only

Answer 1

Answer: (D)

$[C]=\left[M^{-1}{L}^{-2}{T}^4{A}^2\right],[R]=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
$[L]=\left[M{L}^2{T}^{-2}{A}^{-2}\right]$ and $[I]=\left[M^0{L}^0{T}^{0}A\right]$
$(1)[CR]=\left[M^{-1}{L}^{-2}{T}^4{A}^2\right]\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
$=\left[M^0{L}^{0}T{A}^0\right]$
(2) $\left[\frac{L}{R}\right]=\frac{\left[M{L}^2{T}^{-2}{A}^{-2}\right]}{\left[M{L}^2{T}^{-3}{A}^{-2}\right]}$
$=\left[M^0{L}^{0}T{A}^0\right]$
(3) $[\sqrt{LC}]={\left(\left[M{L}^2{T}^{-2}{A}^{-2}\right]\times \left[M^{-1}{L}^{-2}{T}^4{A}^2\right]\right)}^{1/2}$
$=\left[M^0{L}^{0}T{A}^0\right]$
(4) $\left[L{I}^2\right]=\left[M{L}^2{T}^{-2}{A}^{-2}\right]{\left[M^0{L}^0{T}^0{A}^0\right]}^2$
$=\left[M{L}^2{T}^{-2}{A}^0\right]$