Physics

Problem

A junction is supplied by two time-dependent currents directed toward the node:

\displaystyle I_a(t)=4.0\,\text{mA}+2.0\,t\,\text{mA}

and

\displaystyle I_b(t)=3.0\,\text{mA}\,\sin(\pi t)

, where

t

is measured in seconds. A third branch leaves the junction carrying an unknown current

I_x(t)

away from the node. (a) Derive an expression for

I_x(t)

that ensures the conservation of charge at every instant. (b) Determine the numerical value (with units and sign) of

I_x

t=2.0\,\text{s}

. (c) State explicitly whether the current found in part (b) is directed toward or away from the junction and justify your answer based on its sign.