Question

the amount of charge passed in time t through a cross-section of a wire Q(t)=4t²+3t+1 where q is in coulomb and t is in second. the value of current at t=2s is​

Answer 1

Current = Rate of flow of charges.

$\boxed{\rm i = \dfrac{dQ}{dt}}$

Now, solve it by simple differentiation:

$\longrightarrow\rm i = \dfrac{dQ}{dt}$

$\longrightarrow\rm i = \dfrac{d(4t^2 + 3t +1)}{dt}$

$\longrightarrow\rm i = (2)4t + 3(1) +0$

$\longrightarrow\rm i = 8t + 3$

• value of current at t=2s

$\longrightarrow\rm i = 8(2) + 3$

$\longrightarrow\rm i = 16+ 3 = 19\: A$

so, the value of current at t=2s is 19A.