https://file.aiquickdraw.com/mathbot/file/1726056701537ysigtbf8.jpg

Let's analyze the circuit from the image you've provided and solve for the required values.

### Circuit Information:
1. **Resistors:**
   - \( R_1 = 20 \, \Omega \)
   - \( R_2 = 30 \, \Omega \)
   - \( R_3 = 50 \, \Omega \)
   - \( R_4 = 100 \, \Omega \) (in parallel with \( R_5 \))
   - \( R_5 = 300 \, \Omega \)
   
2. **Voltage Source:** \( V = 20 \, V \).

### To solve:
- **Step 1: Simplify the Parallel Combination of \( R_4 \) and \( R_5 \):**

   The combined resistance \( R_{45} \) for resistors \( R_4 \) and \( R_5 \) in parallel is given by the formula:
   \[
   \frac{1}{R_{45}} = \frac{1}{R_4} + \frac{1}{R_5}
   \]

- **Step 2: Find the Total Resistance in the Circuit:**

   The combined resistance \( R_{45} \) is in series with \( R_2 \) and in parallel with the branch containing \( R_1 \) and \( R_3 \). We'll compute the equivalent resistance for the whole circuit.

- **Step 3: Calculate the Current in the Circuit:**

   Using Ohm's law, once we find the total resistance, we can determine the current flowing from the 20V source.

- **Step 4: Determine Voltage Drops:**
   With the current known, calculate the voltage drops across various components to find the voltages across AC and BC, and the current through \( R_2 \).

Let me proceed with the detailed calculations.### Solution:

1. **Equivalent Resistance of \( R_4 \) and \( R_5 \) in Parallel:**
   \[
   R_{45} = 75 \, \Omega
   \]

2. **Total Resistance of the Circuit:**
   \[
   R_{\text{total}} = 66.21 \, \Omega
   \]

3. **Total Current in the Circuit:**
   \[
   I_{\text{total}} = 0.302 \, \text{A}
   \]

4. **Voltage Across BC (across \( R_1 \) and \( R_3 \)):**
   \[
   V_{BC} = 21.15 \, V
   \]

5. **Current Through \( R_2 \):**
   \[
   I_{R_2} = 0.302 \, \text{A}
   \]

6. **Voltage Across AC (across \( R_2 \)):**
   \[
   V_{AC} = 9.06 \, V
   \]

This provides the voltages across AC and BC and the current flowing through \( R_2 \). Let me know if you'd like further explanation on any of these steps or if you have additional questions.

Here are 5 related questions for further practice:
1. How would the total current change if \( R_1 \) were increased to 40Ω?
2. What is the power dissipated in \( R_2 \)?
3. What would happen to the total resistance if \( R_5 \) were removed from the circuit?
4. How much voltage would be across \( R_4 \)?
5. If the voltage were doubled to 40V, how would the voltage across AC change?

**Tip:** When resistors are in parallel, the total resistance is always less than the smallest individual resistance.

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

Learn how to determine the voltages across AC, BC, and the current flow through R2 in a circuit using Ohm's Law, and the rules for resistors in series and parallel. Step-by-step calculations included.

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