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A quatity X is given by ε0 L ΔV/Δt , where ε0 is the permittivity of free space, L is a length, ΔV is potential difference and Δt is the time interval. The dimensional formula for X is the same as that of
  • a)
    resistance
  • b)
    charge
  • c)
    voltage
  • d)
    current
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A quatity X is given by ε0 L ΔV/Δt , where &epsilo...
0 L] = [capacitance] = [C]
∴ X = ε0L ( ΔV/Δt ) = CΔV/Δt = ΔQ/Δt = current
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A quatity X is given by ε0 L ΔV/Δt , where &epsilo...
Dimensional Analysis of Quantity X:
Given quantity X is expressed as ε0 L ΔV/Δt, where ε0 is the permittivity of free space, L is a length, ΔV is potential difference, and Δt is the time interval.

Dimensional Formula for X:
To find the dimensional formula for X, we substitute the dimensions of the given quantities:
- ε0 is the permittivity of free space, which has dimensions [M^-1 L^-3 T^4 A^2].
- L is a length, which has dimensions [L].
- ΔV is potential difference, which has dimensions [M L^2 T^-3 A^-1].
- Δt is the time interval, which has dimensions [T].
Therefore, the dimensional formula for X is [M L T^-3 A^-1].

Comparison with Physical Quantities:
- Resistance has dimensions [M L^2 T^-3 A^-2].
- Charge has dimensions [A T].
- Voltage has dimensions [M L^2 T^-3 A^-1].
- Current has dimensions [A].
The dimensional formula for quantity X matches with the dimensional formula of current, making option 'D' (current) the correct answer.
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A quatity X is given by ε0 L ΔV/Δt , where ε0 is the permittivity of free space, L is a length, ΔV is potential difference and Δt is the time interval. The dimensional formula for X is the same as that ofa)resistanceb)chargec)voltaged)currentCorrect answer is option 'D'. Can you explain this answer?
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