If q=q0(1-e(-τ/RC)] Here, q = electric charge, R = electric resistance, C = electric capacitance. The dimensional formula for τ are

Question

If q=q0(1-e(-τ/RC)] Here, q = electric charge, R = electric resistance, C = electric capacitance. The dimensional formula for τ are (A) [A-1MLT-2] (B) [AM0L0T-1] (C) [M0L0T] (D) [M0L0T-2]

Tardigrade Admin · Accepted Answer

[RC] is time constant =[M0L0T] Exponents have no dimensions ∴ (τ/RC)=[M0L0T] ⇒ τ=[M0L0T]

Q. If $q = q_{0} (1 - e^{\frac{- τ}{RC}}]$ Here, $q =$ electric charge, $R =$ electric resistance, $C =$ electric capacitance. The dimensional formula for $τ$ are

$[A^{- 1} M L T^{- 2}]$

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

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

$[M^{0} L^{0} T^{- 2}]$

$[RC]$ is time constant $= [M^{0} L^{0} T]$
Exponents have no dimensions

$∴ \frac{τ}{RC} = [M^{0} L^{0} T]$
$\Rightarrow τ = [M^{0} L^{0} T]$

Q. If q=q0​(1−eRC−τ​] Here, q= electric charge, R= electric resistance, C= electric capacitance. The dimensional formula for τ are

[A−1MLT−2]

[AM0L0T−1]

[M0L0T]

[M0L0T−2]