Practice portal › Alternating Current › AC Through R, L and C
Asked in GUJCET 2007 · Units and dimensions
Given: R resistance, L inductance, C capacitance.
Idea: in a charging R-C circuit, q=q₀(1-e^-t/RC). An exponent can only be a pure number, so RC must have the dimension of time.
The same argument on an L-R circuit, i=i₀(1-e^-Rt/L), makes L/R a time as well.
Check it directly: [R]=M¹L²T⁻³A⁻² and [L]=M¹L²T⁻²A⁻², so ([L])/([R])=T¹.
So RC and L/R share the dimension of time.
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