# Dimensional formula of Capacitance reactance Xc

1
by minaGanesan

2015-09-12T06:40:28+05:30

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X_C = capacitance reactance = 1/(ωC)
Resistance R, Inductive reactance ω L = X_L and capacitative reactance X_C all have the same units - Ohms, Ω..

R = Votage / Current = Power / Current² = Energy / (Time * Current²)
= [M L² T⁻² ] / [T A²]  = [ M ] [ L² ] [ T⁻³ ] [ A⁻² ]
here A stands for Ampere ,  dimension for Current.

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Capacitance : C = Q / V
V = work done / charge moved through potential difference
= Force * Distance / (current * Time)
=  [ M  ] [ L² ] [ T⁻³ ] [ A⁻¹  ]

Q = current * time = [ A ] [ T ]

C =  [ A² ] [ T⁴ ]  [ M⁻¹ ] [ L⁻² ]

ω = angular velocity = radians/sec = [ T⁻¹ ]

Capacitative reactance = X_C = impedance = 1/(ω C) = [ M ] [ L² ] [ A⁻² ] [ T⁻³ ]

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