Answer
$a) \ V_1 = 8V \\ b) \ I = 2A \\ c) \ R_2 = 2\Omega$
Work Step by Step
a) We use Kirchhoff's Voltage Law, which states that the voltage around any closed loop in a circuit is 0, to find:
$4 -12 + V_1 = 0 \\ V_1 - 8 = 0 \\ V_1 = \fbox{8V}$
b) We apply Ohm's law, which states that $I=\frac{V}{R}$, to find:
$I = \frac{8V}{4\Omega} = \fbox{2A}$
c) We use Ohm's law to find:
$I=\frac{V}{R} \\ R=\frac{V}{I} \\ R = \frac{4V}{2A} = 2 \Omega$
