Which of the following circuit diagrams correctly represent the circuit describe

Question

Which of the following circuit diagrams correctly represent the circuit described in this problem? Check all that apply. Learning Goal To practice Problem-Solving Strategy 30.1: Inductors in Circuits. R2 Ri A circuit has a 1.7 V battery connected in series with a switch. When the switch is closed, the battery powers two paths in parallel, one of which has a resistor of resistance R1-85 2 in series with an inductor of inductance L 1.5x102 H, while the other has a resistor of resistance R2 380 2. What is the current supplied by the battery at a time t 0.3 ms after the switch is closed? RI R2

Explanation / Answer

1st and 3rd circuit diagrams are the correct answer.

from the first diagram,

after a longt time, i2_max = V/R1 = 1.7/85 = 0.02 A

i3 = V/R2 = 1.7/380 = 0.00447 A

i1 = i2_max + i3

= 0.02 + 0.00447

= 0.02447 A

Time constant of the circuit, T = L/R1

= 1.5*10^-2/85

= 0.176 ms

atime t = 0.3 ms

i2 = i2_max*(1 - e^(-t/T))

= 0.02*(1 - e^(-0.176/0.3))

= 0.00887 A

so, i1 = i2 + i3

= 0.00887 + 0.00447

= 0.0133 A

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