Question

The amount of charge Q passed in time t through a cross-section of a wire is $Q = 5{t^2} + 3t + 1$. The value of current at time t=5 s is
A) 9 A
B) 49 A
C) 53 A
D) None of these

Answer 1

Hint:This question is from electricity. The problem is solved by the Electric Current concept. Apply the Electric Current equation to find the current (I) at the given time (t)

Formula Used:
$I = \dfrac{{dQ}}{{dt}}$
Where,
I = Current
Q = Charge
t = time


Complete answer:
The differential limit gives the current at any instant if the rate of charge flow is not constant:
$I = \dfrac{{dQ}}{{dt}}$
\[I = \dfrac{{d(5{t^2} + 3t + 1)}}{{dt}}\]
\[I = 10t + 3\]
\[I = 10 \times 5 + 3 = 53\]A

Hence, the correct option is Option C) 53 A.

Additional Information:
i) The electric current is a flow of charged particles (electrons) through wires and other components.
ii) Electric current is the rate of flow of charge.
iii) Electric current flows from the negative terminal of the cell to the positive terminal.
iv) The conventional direction of electric current is taken as opposite to the direction of the flow of charge (electrons).




Note: The S.I unit of charge is coulomb and the S.I unit of electric current is ampere (coulomb per second). Pay attention to the units while putting all the values in the questions.