Four conductors meet at node P inside a complex circuit

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

Problem

Four conductors meet at node P inside a complex circuit. The currents in three of the conductors are known symbolically: •

I_1

enters the node. •

I_2

leaves the node. •

I_3

also leaves the node. The current in the fourth conductor,

I_4

, is unknown. Throughout normal operation,

I_1

varies with time according to

I_1(t)=I_0\sin(\omega t)

, where

I_0

and

\omega

are constants. Currents

I_2

and

I_3

are constant in time. (a) Derive an algebraic expression for

I_4(t)

in terms of

I_0

\omega

t

I_2

, and

I_3

. (b) Assuming

I_0=4.0\,\text{A}

I_2=1.5\,\text{A}

I_3=2.0\,\text{A}

, and

\omega=120\,\text{rad}\,\text{s}^{-1}

, determine the earliest time

t>0

at which the current in the fourth conductor reverses direction. Show all steps in your reasoning. (c) Explain, without additional calculations, how the waveform of

I_4(t)

would change if

I_2

and

I_3

were both doubled while

I_1(t)

remained the same.

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