Figure $2$: Figure for problem $3.$

$3.)$ Determine $($a$.)$ the equivalent resistance of the circuit shown in Figure $2,($b$.)$ the voltage across each resistor and $($c$.)$ the current through each resistor.

$4.)$ Determine the magnitudes and directions of the currents in each resistor in Figure $3$ for each case: $($a$.)$ Ignoring internal resistance of the batteries and $($b$.)$ Assume each battery has an internal resistance of $r=1\mathrm{.}0.$