Answer
a) $v_1 + v_2 = v$
b) $v_1 = 3I; v_2 = 4I $
c) $v = 14V$
d) Power is conserved.
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:
$-v + v_1 + v_2 = 0 \\ v = v_1 + v_2$
b) We know from Ohm's law that $V=IR$. Thus, plugging in the values for resistance, we find: $v_1 = 3I; v_2 = 4I $
c) We know that there is a current of 2A, so we use the results from parts a and b to find:
$v = 3I + 4I \\ v = 7I \\ V = 7(2) = \fbox{14V}$
d) We know that the power across a circuit is conserved, for energy is conserved. (If you want to verify this, you can use the equation for power to find the power of each circuit element: it will add up to 0W.)
