If L, R, C denote inductance, resistance and capacitance, respectively. Then dimensions of (L/R2C) are

Question

If L, R, C denote inductance, resistance and capacitance, respectively. Then dimensions of (L/R2C) are (A) [M0L0T] (B) [MLT-1] (C) [A-1M0L0T-1] (D) [M0L0T0]

Tardigrade Admin · Accepted Answer

(L/R)= time constant of L-R circuit =[M0L0T] RC = time constant of R-C circuit =[M0L0T] ∴ The dimensions of (L2/R2C)=((L/R))×(1/RC) =([M0L0T]/M0L0T)=[M0L0T0]

Q. If $L, R, C$ denote inductance, resistance and capacitance, respectively. Then dimensions of $\frac{L}{R ^{2} C}$ are

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

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

$[A^{- 1} M^{0} L^{0} T^{- 1}]$

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

$\frac{L}{R} =$ time constant of $L - R$ circuit $= [M^{0} L^{0} T]$

$RC =$ time constant of $R - C$ circuit $= [M^{0} L^{0} T]$

$∴$ The dimensions of

$\frac{L ^{2}}{R ^{2} C} = (\frac{L}{R}) \times \frac{1}{RC}$
$= \frac{[ M ^{0} L ^{0} T ]}{M ^{0} L ^{0} T} = [M^{0} L^{0} T^{0}]$

Q. If L,R,C denote inductance, resistance and capacitance, respectively. Then dimensions of R2CL​ are

[M0L0T]

[MLT−1]

[A−1M0L0T−1]

[M0L0T0]