Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T and C stand for unit of mass, length, time and charge, [2025]

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Q.
Which one of the following is the correct dimensional formula for the capacitance in F M, L, T and C stand for unit of mass, length, time and charge, [2025]

1 $[F] = [C^{2} M^{- 2} L^{2} T^{2}]$

2 $[F] = [C M^{- 2} L^{- 2} T^{- 2}]$

3 $[F] = [C M^{- 1} L^{- 2} T^{2}]$

4 $[F] = [C^{2} M^{- 1} L^{- 2} T^{2}]$

Ans.
(4)

$C = \frac{q}{V} = \frac{q}{V} \cdot \frac{q}{q} = \frac{q^{2}}{Work done}$

$∴ [F] = \frac{[C^{2}]}{[M L^{2} T^{- 2}]} = [C^{2} M^{- 1} L^{- 2} T^{2}]$

Solution

Q.
Which one of the following is the correct dimensional formula for the capacitance in F M, L, T and C stand for unit of mass, length, time and charge, [2025]

1 $[F] = [C^{2} M^{- 2} L^{2} T^{2}]$

2 $[F] = [C M^{- 2} L^{- 2} T^{- 2}]$

3 $[F] = [C M^{- 1} L^{- 2} T^{2}]$

4 $[F] = [C^{2} M^{- 1} L^{- 2} T^{2}]$

Ans.
(4)

$C = \frac{q}{V} = \frac{q}{V} \cdot \frac{q}{q} = \frac{q^{2}}{Work done}$

$∴ [F] = \frac{[C^{2}]}{[M L^{2} T^{- 2}]} = [C^{2} M^{- 1} L^{- 2} T^{2}]$

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Solution

Q. Which one of the following is the correct dimensional formula for the capacitance in F M, L, T and C stand for unit of mass, length, time and charge, [2025]

1 [F]=[C2M–2L2T2]

2 [F]=[CM–2L–2T–2]

3 [F]=[CM–1L–2T2]

4 [F]=[C2M–1L–2T2]

Ans. (4) C=qV=qV·qq=q2Work done ∴ [F]=[C2][ML2T–2]=[C2M–1L–2T2]

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Q.
Which one of the following is the correct dimensional formula for the capacitance in F M, L, T and C stand for unit of mass, length, time and charge, [2025]

1 $[F] = [C^{2} M^{- 2} L^{2} T^{2}]$

2 $[F] = [C M^{- 2} L^{- 2} T^{- 2}]$

3 $[F] = [C M^{- 1} L^{- 2} T^{2}]$

4 $[F] = [C^{2} M^{- 1} L^{- 2} T^{2}]$

Ans.
(4)

$C = \frac{q}{V} = \frac{q}{V} \cdot \frac{q}{q} = \frac{q^{2}}{Work done}$

$∴ [F] = \frac{[C^{2}]}{[M L^{2} T^{- 2}]} = [C^{2} M^{- 1} L^{- 2} T^{2}]$