Amount of charge passing through the cross section of a wire is `q(t) = at^(2) + bt + c`. Write the dimensional formula for a,b and c. If the values of a,b and C in SI units are 6,4,2 respectively, find the value of current at t = 6 seconds

Explanation

Charge passing through wire is given by `q (t) = at^(2) + bt + c`
According to principle of homogenity,
Dimensional formula of
q(t) = dimensional formula of `at^(2)`
`IT = aT^(2)`
`:.` Dimensional formula `a = IT^(-1)`
Dimensional formula of q(t)
Dimensional formula of bt
IT = BT
`:.` Dimensional formula of b = 1
Dimensional formula of
q(t) = dimensiona formula of C.
IT = C
`:.` Dimensonal formula of C = IT
Current, `I = (dq(t))/(dt) = (d)/(dt) [at^(2) + bt + c)`
= at + b
Here a = 6 and b = 4
`implies I = 12 t + 4`
`:.` Current at t = 6 sec
`I = 12 xx 6 + 4 = 76 A`.