QUANTUM BIOLOGY - EXAMPLE 33.3 : In quantum biology, microtubule is used to store information in a cell. At temperature of T = 300 K, measured current I in a probe is directly proportional to the supplied voltage V, when passing through a microtubule with resistance R. (a) Form an equation of V as a function of I involving k as a constant. (b) If the microtubule has R = 1 ohm at such condition, find the value of V when I = 2 A. Hint : Ohm's law. (c) Find the relationship of k as a function of R.
QUANTUM BIOLOGY - ANSWER 33.3 : (a) Let I = kV, V = I / k. (b ) By Ohm's law, when I = 2 A, V = IR = 2 A x 1 ohm = 2 V. (c) From answers in (a) and (b), V = I / k = IR. Then k = 1 / R. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 55 - The differential equation is 3 dy / dt + 2y = 1 with y(0) = 1. (a) The Laplace transformation, L for given terms are : L (dy / dt) = sY(s) - y(0), L(y) = Y(s), L(1) = 1 / s. Use such transformation to find Y(s). (b) The initial value theorem states that : When t approaches 0 for a function of y(t), it is equal to a function of sY(s) when s approaches infinity. Use the initial value theorem as a check to the answer found in part (a).
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