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The amount of charge passed in time t through a cross-section of a wire is Q(t) = At^2 + Bt + C. (a) Write the dimensional formulae for A, B and C. (b) If the numerical values of A, B and C are 5, 3 and 1 respectively in SI units, find the value of the current at t = 5 s.

The amount of charge passed in time t through a cross-section of a wire is
Q(t) = At^2 + Bt + C.
(a) Write the dimensional formulae for A, B and C.
(b) If the numerical values of A, B and C are 5, 3 and 1 respectively in SI units, find the value of the current at t = 5 s.

Grade:10

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Sol. Q(t) = At^2 + Bt + c a) At^2 = Q ⇒ A = Q/t^2 = ‘T’/T^-2 = A 1^T^-1 b) Bt = Q ⇒ B = Q/t = A ‘T’/T = A c) C = [Q] ⇒ C = A’T’ d) Current t = dq/dt = d/dt(At^2 + Bt + C) = 2At + B = 2 * 5 * 5 + 3 = 53 A.

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