The charge flowing in a conductor changes with time as Q t = α t - β t 2 + γ t 3 , where α , β and γ are constants. Minimum value of current is:

Step-by-step solution

Given here, Q = α t - β t 2 + γ t 3 Current flowing through conductor is given by i = d Q d t = α - 2 β t + 3 γ t 2         . . . 1 For current to be minimum, d i d t = 0 So, d i d t = 6 γ t - 2 β = 0 ⇒ t = β 3 γ Substituting in equation (1), i = α - 2 β t + 3 γ t 2 = α - 2 β β 3 γ + 3 γ β 3 γ 2 = α - 2 β 2 3 γ + 3 β 2 9 γ = α - β 2 3 γ