A single junction J connects three branches in a portable charging station

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Circuits · Electric Circuits

Problem

A single junction J connects three branches in a portable charging station. Branch 1 carries a constant current

I_1 = 2.0\,\text{A}

into the junction. Branch 2 carries a time-dependent current

I_2(t)

out of the junction, where

I_2(t)

is described by the following piecewise linear function of time

t

(in seconds): • From

t=0

t=2\,\text{s}

I_2(t)

increases uniformly from

0

3.0\,\text{A}.

• From

t=2\,\text{s}

t=4\,\text{s}

I_2(t)

decreases uniformly back to

0\,\text{A}.

(No current flows in branch 2 outside the interval

0\le t\le 4\,\text{s}

.) Branch 3 carries current

I_3(t)

whose magnitude and direction may vary with time. (a) Sketch qualitatively accurate graphs of

I_1

I_2(t)

, and

I_3(t)

on the same set of axes for the interval

0\le t\le 4\,\text{s}

. Clearly label magnitudes, directions (positive into the junction), and key time points. (b) Derive an expression for

I_3(t)

for each of the two time intervals

0\le t\le 2\,\text{s}

and

2\le t\le 4\,\text{s}

. (c) Calculate the net charge that enters the junction through branch 3 during the entire

4\,\text{s}

interval. Express your answer in coulombs and indicate whether net charge is entering or leaving the junction through branch 3. (d) Explain how your result in part (c) would change if the constant current in branch 1 were doubled while the function

I_2(t)

remained the same.

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