The work done by a battery is W=ε Δ q, where Δ q charge transferred by battery, ε= emf of the battery. What are dimensions of emf of battery?

Question

The work done by a battery is W=ε Δ q, where Δ q charge transferred by battery, ε= emf of the battery. What are dimensions of emf of battery? (A) [ M 0 L 0 T -2 A -2] (B) [M L2 T-3 A-2] (C) [ M 2 L 0 T -3 A 0] (D) [ ML 2 T -3 A -1]

Tardigrade Admin · Accepted Answer

Work done, W=ε Δ q ∴ ε=(W/Δ q)=([M L2 T-2]/[ AT ]) ∴ [ε] =[M L2 T-3 A-1]

Q. The work done by a battery is $W = ε Δ q$ , where $Δ q$ charge transferred by battery, $ε =$ emf of the battery. What are dimensions of emf of battery?

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

$[M L^{2} T^{- 3} A^{- 2}]$

$[M^{2} L^{0} T^{- 3} A^{0}]$

$[M L^{2} T^{- 3} A^{- 1}]$

Work done, $W = ε Δ q$
$∴ ε = \frac{W}{Δ q} = \frac{[ M L ^{2} T ^{- 2} ]}{[ A T ]}$
$∴ [ε] = [M L^{2} T^{- 3} A^{- 1}]$

Q. The work done by a battery is W=εΔq, where Δq charge transferred by battery, ε= emf of the battery. What are dimensions of emf of battery?

[M0L0T−2A−2]

[ML2T−3A−2]

[M2L0T−3A0]

[ML2T−3A−1]