First slide

Dimensions of physical quantities

Question

If L and R denote inductance and resistance respectively, then the dimensional formula of L/R is:

Moderate

A

$M^{1} L^{0} T^{0} Q^{- 1}$
B

$M^{0} L^{0} T Q^{0}$
C

$M^{0} L^{1} T^{- 1} Q^{0}$
D

$M^{- 1} L T^{0} Q^{- 1}$

Solution

time constant DURING the growth of LR CIRCUIT IS $τ = \frac{L}{R}$ In M(meter)-K(kilogram)-S(second)-Q(charge) system,
SO $\frac{L}{R} w i l l h a v e t h e d i m e n s i o n s o f t i m e .$
Energy stored in inductor is $U = \frac{1}{2} L i^{2}$
Heat developed in resistor is, $H = i^{2} R t$ ;
Equating both L=Rt or L/R= t. (or)
Dimension of L $= [M^{1} L^{2} T^{0} Q^{- 2}]$
Dimension of R $= [M^{1} L^{2} T^{- 1} Q^{- 2}]$
Dimension of L/R $= \frac{[M^{1} L^{2} T^{0} Q^{- 2}]}{[M^{1} L^{2} T^{- 1} Q^{- 2}]} = [M^{0} L^{0} T Q^{0}]$

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