$($a$)$

At top left, vertical voltage source V$1$ is connected in series with Voltage source V$2$ below, both positive end up$,$ so the total voltage top to bottom is V$1+$ V$2.$ The top of V$1$ connects to left end of horizontal R$1,$ whose right end connects to an SPST switch S$1$ that closes at t$=0.$ The bottom of V$1$ connects to left end of horizontal R$3,$ whose right end connects to the lever of an SPDT switch S$2$ that moves from position $1$ to position $2$ at t$=2$ sec$.$ The bottom of V$2$ connects to left end of horizontal R$6,$ whose right end connects to an SPST S$3$ switch that opens at t$=0$ sec$.$ Vertical resistor R$4$ at right connects at top to the right side of S$1,$ and at bottom to the right side of S$3.$ The top of R$4$ also connects via diagonal resistor R$2$ to terminal $1$ of S$2,$ and the bottom of R$4$ connects via diagonal resistor R$5$ to terminal $2$ of S$2.$

For the circuit above, generate circuit diagrams that include only those elements that have current flowing through them for:

$1)$ t $<0$

$2)0<$ t $<2$ s

$3)$ t $>2$ s