Answer
a) $I = I_1 + I_2 $
b) $I_1 = \frac{v}{15}; I_2 = \frac{v}{10}$
c) $v=24V$
d) Power is conserved.
Work Step by Step
a) Using Kirchhoff's Law, we find the current: $I = I_1 + I_2 $
b) Using the result from part a as well as Ohm's law, which states that $I=\frac{V}{R}$, we obtain:
$I_1 = \frac{v}{15}; I_2 = \frac{v}{10}$
c) We use the fact that $I=4A$ to find:
$ 4 = \frac{v}{15} + \frac{v}{10} \\ 4 = \frac{5v}{30} \\ 5v = 120 \\ \fbox{v=24V}$
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 $0W$.)
