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Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
  • a)
    [M L2T−2]
  • b)
    [M L2T−1I−1]
  • c)
    [M L2T−3I−2]
  • d)
    [M L2T−3I−1].
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Dimensions of resistance in an electrical circuit, in terms of dimens...

Dimensional Analysis of Resistance:

Given Dimensions:
- Mass (M)
- Length (L)
- Time (T)
- Current (I)

Formula for Resistance:
Resistance (R) = ρ * (L/A)
Where,
ρ = resistivity of the material
L = length of the conductor
A = cross-sectional area of the conductor

Dimensional Analysis:
- Resistivity (ρ) = [MLT^-3I^-2]
- Length (L) = [L]
- Area (A) = [L^2]
- Current (I) = [I]

Substitute the Dimensions:
Resistance (R) = ρ * (L/A)
R = [MLT^-3I^-2] * [L] / [L^2]
R = [M L^2 T^-3 I^-2]

Therefore, the dimension of resistance in an electrical circuit, in terms of mass (M), length (L), time (T), and current (I) is [M L^2 T^-3 I^-2], which corresponds to option 'c'.
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Community Answer
Dimensions of resistance in an electrical circuit, in terms of dimens...
According to Ohm's law,
V = RI or R = V/I
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