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# Answer to Question #226856 in Electrical Engineering for rana

Question #226856

Find the charge q(t) flowing through an element if the current is

i(t) = 3e

−t + 20 cos(15t − π

6

⁄ )uA

q(0) = 1uC

1
2021-08-18T09:06:01-0400

"i(t)= 3e^{-t}+20\\:cos\\left(15t-\\frac{\\pi }{6}\\right)\\\\\nq= \\int i(t) dt\\\\\n\\int \\:3e^{-t}+20\\cos \\left(15t-\\frac{\\pi }{6}\\right)dt\\\\\n\\mathrm{Apply\\:the\\:Sum\\:Rule}:\\quad \\int f\\left(x\\right)\\pm g\\left(x\\right)dx=\\int f\\left(x\\right)dx\\pm \\int g\\left(x\\right)dx\\\\\n=\\int \\:3e^{-t}dt+\\int \\:20\\cos \\left(15t-\\frac{\\pi }{6}\\right)dt\\\\\n=-3e^{-t}+\\frac{4}{3}\\sin \\left(15t-\\frac{\\pi }{6}\\right)\\\\\n=-3e^{-t}+\\frac{4}{3}\\sin \\left(15t-\\frac{\\pi }{6}\\right)+C\\\\\nq(0) = 1uC \\implies c=-\\frac{4}{3}\\\\\nq=-3e^{-t}+\\frac{4}{3}\\sin \\left(15t-\\frac{\\pi }{6}\\right)-\\frac{4}{3}\\\\"

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