The charge flowing in a conductor changes with time as Q(t)=α t-β t 2+γ3. Where α, β and γ are constants. Minimum value of current is :

Question

The charge flowing in a conductor changes with time as Q(t)=α t-β t 2+&gamma;3. Where α, β and &gamma; are constants. Minimum value of current is : (A) α-(&gamma;2/3 β) (B) β-(α2/3 &gamma;) (C) α-(β2/3 &gamma;) (D) α-(3 β2/&gamma;)

Tardigrade Admin · Accepted Answer

Q =(α t -β t 2+&gamma; t 3) i =( dQ / dt )=(α-2 β t +3 &gamma; t 2) ( di / dt )=(3 &gamma; t -2 β)=0 ⇒ t =(β/3 &gamma;) i =(α-2 β t +3 &gamma; t 2)=(α-(β2/3 &gamma;))

Q. The charge flowing in a conductor changes with time as $Q (t) = α t - β t^{2} + γ^{3}$ . Where $α, β$ and $γ$ are constants. Minimum value of current is :

$α - \frac{γ ^{2}}{3 β}$

$β - \frac{α ^{2}}{3 γ}$

$α - \frac{β ^{2}}{3 γ}$

$α - \frac{3 β ^{2}}{γ}$

$Q = (α t - β t^{2} + γ t^{3})$
$i = \frac{d Q}{d t} = (α - 2 βt + 3 γ t^{2})$
$\frac{d i}{d t} = (3 γ t - 2 β) = 0$
$\Rightarrow t = \frac{β}{3 γ}$
$i = (α - 2 βt + 3 γ t^{2}) = (α - \frac{β ^{2}}{3 γ})$

Q. The charge flowing in a conductor changes with time as Q(t)=αt−βt2+γ3. Where α,β and γ are constants. Minimum value of current is :

α−3βγ2​

β−3γα2​

α−3γβ2​

α−γ3β2​