Answer:
(a) - [tex]R_{eq.}=8 \ \Omega[/tex]
(b) - [tex]I_1=3 \ A, \ I_2= 1.8 \ A, \ I_3=1.2 \ A[/tex]
(c) - [tex]\Delta V_1=6 \ V, \ \Delta V_2= 18\ V, \ \Delta V_3= 18 \ V[/tex]
Conceptual:
Things to know about parallel/series resistors:
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Resistors in Series:}}\\\\R_s=R_1+R_2+R_3+\dots +R_n\\\\I_1=I_2=I_3= \dots = I_n\\\\\Delta V_1+\Delta V_2+\Delta V_3+ \dots +\Delta V_n=\Delta V\end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Resistors in Parallel:}}\\\\\frac{1}{R_p}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+ \dots + \frac{1}{R_n} \\\\\Delta V_1=\Delta V_2=\Delta V_3= \dots =\Delta V_n\\\\I_1+I_2+I_3+ \dots + I_n=I\end{array}\right}[/tex]
What is a resistor?
A resistor takes electrical energy and converts it to some other form of energy, such as heat. In doing so this can alter a circuit's current and divide voltages.
What is current?
Electrical current is the flow of charged particles.
What is voltage?
To put it simply, voltage is what "pushes" current through a circuit.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Ohm's Law:}}\\\\\Delta V=IR\end{array}\right}[/tex]
How you should tackle these types of problems:
I recommend combining resistors until you have one resistor. This one resistor is what your total resistance is, which I call the equivalent resistor. Then work backwards from the equivalent resistor to find any information you need, utilizing Ohm's law and properties of parallel/series resistors.
Step-by-step:
Refer to the attached image(s).
