Homework SourseIn an amplified circuit the current i in A changes with time
In an amplified circuit, the current i (in A) changes with timet (in s) according to the equation below. If 0.075 C of charge has passed a point in the circuit at t=0, find the total charge to have passed the point at t=0.15 s.
i=.06t sqrt(1+t^2)
Please show all work so I can learn to do this on my own and if writing please do so legibly so I can read it the pictures on here are small. Thank you :-)
i=.06t sqrt(1+t^2)
Please show all work so I can learn to do this on my own and if writing please do so legibly so I can read it the pictures on here are small. Thank you :-)
Solution
current i = 0.06t (1 + t2) = dq/dt
charge q(t) = idt = 0.06t (1 + t2) dt = 0.03 * (1 + t2) * 2t dt = 0.03 (1 + t2)1/2 d(1 + t2)
= 0.03 * (2/3) (1 + t2)3/2 + C = 0.02 (1 + t2)3/2 + C
since q(0) = 0.075= 0.02+ C, so C = 0.055
q(t) = 0.02 (1 + t2)3/2 + 0.055
so q(0.15)= 0.02 (1 + 0.152)3/2 + 0.055 = 0.075678 C
