Node of a circuit is connected to four branches whose currents are designated and…

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

Problem

Node

N

of a circuit is connected to four branches whose currents are designated and oriented as follows: •

I_1

leaves node

N

through a resistor. •

I_2

leaves node

N

through a different resistor. • A current source sends a fixed

2\,\text{A}

into node

N

. • A dependent current source also sends current into node

N

; its value is

k\,I_1

, where

k

is a constant to be determined. • An additional current source of

1\,\text{A}

draws current out of node

N

(current directed away from

N

). Assume the stated directions to be positive for each branch current. (i) Write the current–balance equation at node

N

and hence obtain an expression for the constant

k

in terms of

I_1

and

I_2

. (ii) If steady–state measurements yield

I_1 = 5\,\text{A}

and

I_2 = 3\,\text{A}

, calculate the numerical value of

k