The current in the conductor changes over time according to the law I = 3 + 2t + 0.5t ^ 2 (A). What charge will pass through the cross-section of the conductor in the time from t1 = 2 s to t2 = 6 s? At what strength of direct current will the same charge pass through the cross-section of the conductor during the same period of time?
I (t) = 3 + 2 * t + 0.5 * t ^ 2.
t1 = 2 s.
t2 = 6 s.
The dependence of the charge on time q (t) is an integral of the dependence of the current strength on time I (t): q (t) = ∫I (t).
q (t) = ∫ (3 + 2 * t + 0.5 * t ^ 2) = 3 * t + t2 + t3 / 6.
q = q (t2) – q (t1).
q (6 s) = 3 * 6 + (6) ^ 2 + (6) 3/6 = 90 Cl.
q (2 s) = 3 * 2 + (2) ^ 2 + (2) 3/6 = 11.3 Cl.
q = 90 Cl – 11.3 Cl = 78.7 Cl.
The strength of the direct current Ipost is determined by the formula: Ipost = q / (t2 – t1).
Ipost = 78.7 C / (6 s – 2 s) = 19.7 A.
Answer: q = 78.7 C, Ipost = 19.7 A.
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