The current in a wire varies with time according to the equation l=4+2t, where l is in ampere and t is in sec. the quantity of charge which has passed through a cross-section of the wire during the time t=2 sec to t=6 sec will be

Options

A. 40C
B. 48C
C. 38C
D. 43C

Answer

B

Explanation

Let dq be the charge which passes in a small interval of time dt. Then
dt=Idt
or dq=(4+2t)dt
On integrating, we get
`q=underset(2)overset(6)(int)(4+2t)dt=[4t+t^(2)]_(2)^(6)=48C`