The charge flown through a circuit in the time interval between t and t+dt is given by $d q = e^{- t / τ} d t$ , where $τ$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $τ$

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If charge flown through a wire is given by q=3sin(3t), then find out the current flown through the wire at t=π9 seconds.

The correct option is A 4.5 ARate of charge flow w.r.t. time is current, ∴i=dqdt=3×3cos(3t) ⇒i|t=π9=9cos(3.π9)=9cos(π3)=92=4.5 A i=4.5 A

If charge flown through a wire is given by $q = 3 sin (3 t)$ , then find out the current flown through the wire at $t = \frac{π}{9}$ seconds.

The correct option is A $4.5 A$
Rate of charge flow w.r.t. time is current,

$∴ i = \frac{d q}{d t} = 3 \times 3 cos (3 t)$
$\Rightarrow i |_{t = \frac{π}{9}} = 9 cos (3. \frac{π}{9}) = 9 cos (\frac{π}{3}) = \frac{9}{2} = 4.5 A$

$i = 4.5 A$