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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.

Consider the circuit below, determine the voltages across AC, BC, and the current flow through R2.

Solve this circuit problem involving series and parallel resistors to find voltages across points AC and BC and the current through R2 using Ohm's Law and Kirchhoff's Voltage Law. This solution includes step-by-step calculations for a 20V circuit with resistors R1, R2, R3, R4, and R5.

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