a$)$ A simple series DC circuit is given in Figure $1$:

Figure $1$

Determine;

$($i$)$ The total resistance seen by the battery.

$($ii$)$ The circuit current.

$($iii$)$ The voltage across R$2.$

$($iv$)$ The power developed in R$2$

$($v$)$ An engineer is considering replacing R$2$ with a resistor of lower value. Explain the effect this will have on your answers to each of parts $($i$)$ to $($iv$)$