The graph of (entering a junction) versus time is described verbally as follows: from…

PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity

Problem

The graph of

I_1(t)

(entering a junction) versus time is described verbally as follows: from

t=0

t=2\,\text{s}

the current is constant at

6.0\,\text{mA}

; from

t=2\,\text{s}

t=5\,\text{s}

the current decreases linearly to

0

. A second branch carries a current

I_2(t)=2.0\,\text{mA}

toward the junction for the entire interval

0\le t\le5\,\text{s}

. The only branch leaving the junction carries current

I_3(t)

away from the node. (a) Write an explicit piece-wise expression for

I_1(t)

over the interval

0\le t\le5\,\text{s}

. (b) Determine the function

I_3(t)

that satisfies charge conservation for all

0\le t\le5\,\text{s}

. (c) Calculate the total charge that passes through the branch carrying

I_3

during the time interval

0\le t\le5\,\text{s}

. (d) Using your result from part (c) and appropriate reasoning, show that no net charge accumulates at the junction over the given time interval.