To solve the given circuit problem, we will follow these steps:

1. Identify the configuration:

   • $R_4 = 100 \Omega$ and $R_5 = 300 \Omega$ are in parallel.
   • $R_2 = 30 \Omega$ is in series with $R_4$ and $R_5$.
   • $R_3 = 50 \Omega$ and $R_1 = 20 \Omega$ are in series with the rest of the circuit.

2. Find the equivalent resistance of $R_4$ and $R_5$ (parallel combination): The formula for resistances in parallel is: $\frac{1}{R_{45}} = \frac{1}{R_4} + \frac{1}{R_5}$ where $R_4 = 100 \Omega$ and $R_5 = 300 \Omega$.

3. Calculate the total resistance: The total resistance of the circuit will include the series combination of $R_2$, $R_3$, $R_1$, and the parallel combination $R_{45}$.

4. Calculate the total current: Using Ohm's law, $I = \frac{V}{R_{\text{total}}}$, where $V = 20V$.

5. Calculate the voltages across different points:

   • Voltage across $AC$ (which includes $R_2$, $R_3$, and $R_1$).
   • Voltage across $BC$ (which includes $R_3$ and $R_1$).

Let me calculate this step by step.Here are the calculated values for the given circuit:

1. Equivalent resistance of $R_4$ and $R_5$ (parallel combination) = $75 \, \Omega$.
2. Total resistance of the circuit = $175 \, \Omega$.
3. Total current through the circuit = $0.1143 \, \text{A}$ (or $114.3 \, \text{mA}$).
4. Voltage across $AC$ = $11.43 \, \text{V}$.
5. Voltage across $BC$ = $8.00 \, \text{V}$.
6. Current flow through $R_2$ = $0.1143 \, \text{A}$ (same as the total current, since $R_2$ is in series).

Would you like further details or clarifications on any step?

Here are 5 related questions to deepen your understanding:

1. How does changing $R_4$ or $R_5$ affect the total resistance?
2. What would happen to the current if the total voltage is increased to 30V?
3. Can you explain why the current through $R_2$ is the same as the total current?
4. What is the significance of series and parallel resistor combinations in this circuit?
5. How would the voltages across $AC$ and $BC$ change if $R_3$ is halved?

Tip: In parallel circuits, the equivalent resistance is always smaller than the smallest individual resistance.