At t = 0, the open switch in the figure below is thrown closed. We wish to find a symbolic expression for the current in the inductor for time t > 0. Let this current be called i and choose it to be downward in the inductor in the figure below. Identify i1 as the current to the right through R1 and iz as the current downward through R2. R1 R2 (a) Use Kirchhoff's junction rule to find a relation among the three currents. (Use the following as necessary: i1 and i2.) (b) Use Kirchhoff's loop rule around the left loop to find another relationship. (Use the following as necessary: i1, i2, R1, and R2.) (c) Use Kirchhoff's loop rule around the outer loop to find a third relationship. (Use the following as necessary: i1, i2, R1, L, and 1.) dt ll
At t = 0, the open switch in the figure below is thrown closed. We wish to find a symbolic expression for the current in the inductor for time t > 0. Let this current be called i and choose it to be downward in the inductor in the figure below. Identify i1 as the current to the right through R1 and i2 as the current downward through R2.
(a) Use Kirchhoff's junction rule to find a relation among the three currents. (Use the following as necessary: i1 and i2.)
i = ?
(b) Use Kirchhoff's loop rule around the left loop to find another relationship. (Use the following as necessary: i1, i2,R1, and R2.)
emf = ?
(c) Use Kirchhoff's loop rule around the outer loop to find a third relationship. (Use the following as necessary: i1, i2, R1, L, and di/dt)
emf = ?
(d) Eliminate i1 and i2 among the three equations to find an equation involving only the current i. (Use the following as necessary: i, R1, R2, L, E for emf, and di/dt)
0 = ?
(e) Compare the equation in part (d) with E − iR − (L di/dt) = 0 in the text. Use this comparison to rewrite i =(E/R)(1 − e−t/τ) in the text for the situation in this problem and show that i(t) = (E/R1)(1 − e−(R'/L)t) where R' = R1*R2/(R1 + R2).
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