Question

In the following expression, determine the units of the variable , given the units of the other variables: T in seconds (s), Q in coulombs (C), and I in coulombs per second (C/s).

1) x= πQ/VI²

2) x= I√V/T. (square root of V/T)

Answer 1

1) given x= pi Q / V I^2 pi is a number constant it does not have any units. substituting for others we have .Here V is Voltage so unit is Volt(V) dimension of volt is energy/charge = kg m^2 s^(-2)/ C

x = C/ [kg m^2 s^(-2)/C* (C/s)^2] simplifying we get x = s^4 / kg *m^2 this is the unit of x

2) given x = I* = (C/s) * simplifying we get x =C/s *( kg^1/2 m / s C^1/2 s^1/2 )

x = C^1/2 *m*kg^1/2 / s ^5/2

if we keep volt (V) as a standard unit then 1) x = s^2 / V *C.

2 ) x = C/s * V^(1/2) / s^1/2 = C * V^(1/2) /s^3/2