(5%) Problem 2: The excess charge at a given point in a circuit as a function of

Question

(5%) Problem 2: The excess charge at a given point in a circuit as a function of time is described by the equation q(t) = 4.5-2.5t +1.7t. wherc the chargc is in coulombs when the time is in scconds > 50% Part (a) Calculate the instantaneous current, in amperes, that flows through the circuit at time h = 7.5 s Grade Summary Deductions Potential 0% 100% cos0 Submissions Attempts remaining: 20 (0% per attempt) detailed view | tan() acosO) sinh) h) cotanh(O sin cotanasin acotanOsi cosh)tan END °Degrees Radians DELCLEAR Submit Hint ive Hints: 0% deduction per hint. Hints remaining: 1 Feedback: 0% deduction per feedback. 50% Part (b) Calculate the average current, in amperes, that flows through the circuit between t0 = 0 and 1 = 7.5 seconds

Explanation / Answer

Given,

q(t) = 4.5 - 2.5 t + 1.7 t^2

a)We know from the defination of current

I = dq/dt = d(4.5 - 2.5 t + 1.7 t^2)/dt

I(t) = 0 - 2.5 + 3.4 t

for t1 = 7.5

I(t) = -2.5 + 3.4 x 7.5 = 23 A

Hence, I1 = 23 A

b)at t = 0

I(t) = -2.5 A

at t = 7.5

I(t) = 23 A

I(av) = (-2.5 + 23)/2 = 10.25 A

Hence, I(av) = 10.25 A

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