https://file.aiquickdraw.com/mathbot/file/1727201664587d5gzn37t.jpg

The image shows a problem related to combination circuits, where you need to calculate the voltages and currents across four resistors and redraw the circuit.

Here's how to approach the solution:

### Step 1: Analyze the Circuit

From the diagram in the image, it appears to be a combination of series and parallel resistors with the following details:
- **R1 = 100 Ω** (in series with the parallel combination of R2 and R3)
- **R2 = 100 Ω** and **R3 = 100 Ω** (in parallel with each other)
- **R4 = 100 Ω** (in series with the entire circuit)
- The voltage source is **24 V**.

### Step 2: Simplify the Circuit

- **Step 2.1:** Combine the resistances of **R2** and **R3**, which are in parallel:
  \[
  \frac{1}{R_{23}} = \frac{1}{R_2} + \frac{1}{R_3} = \frac{1}{100} + \frac{1}{100} = \frac{2}{100} = \frac{1}{50}
  \]
  So, \( R_{23} = 50 \, \Omega \).

- **Step 2.2:** Now, the simplified circuit has three resistors in series: **R1**, **R23**, and **R4**.
  \[
  R_{\text{total}} = R_1 + R_{23} + R_4 = 100 + 50 + 100 = 250 \, \Omega
  \]

### Step 3: Calculate the Total Current

Using Ohm's law, the total current \( I_{\text{total}} \) is:
\[
I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{24 \, \text{V}}{250 \, \Omega} = 0.096 \, \text{A}
\]

### Step 4: Calculate Voltages Across Each Resistor

Now that we know the total current, we can calculate the voltage drop across each resistor in series:

- **Voltage across R1:**
  \[
  V_{R1} = I_{\text{total}} \times R_1 = 0.096 \, \text{A} \times 100 \, \Omega = 9.6 \, \text{V}
  \]

- **Voltage across R4:**
  \[
  V_{R4} = I_{\text{total}} \times R_4 = 0.096 \, \text{A} \times 100 \, \Omega = 9.6 \, \text{V}
  \]

### Step 5: Voltage and Current for Parallel Resistors R2 and R3

Since \( R2 \) and \( R3 \) are in parallel, they have the same voltage:
\[
V_{R2} = V_{R3} = V_{\text{parallel}} = I_{\text{total}} \times R_{23} = 0.096 \, \text{A} \times 50 \, \Omega = 4.8 \, \text{V}
\]

To find the current through each resistor:
- **Current through R2:**
  \[
  I_{R2} = \frac{V_{R2}}{R_2} = \frac{4.8 \, \text{V}}{100 \, \Omega} = 0.048 \, \text{A}
  \]

- **Current through R3:**
  \[
  I_{R3} = \frac{V_{R3}}{R_3} = \frac{4.8 \, \text{V}}{100 \, \Omega} = 0.048 \, \text{A}
  \]

### Final Results:
- \( V_{R1} = 9.6 \, \text{V}, I_{R1} = 0.096 \, \text{A} \)
- \( V_{R2} = 4.8 \, \text{V}, I_{R2} = 0.048 \, \text{A} \)
- \( V_{R3} = 4.8 \, \text{V}, I_{R3} = 0.048 \, \text{A} \)
- \( V_{R4} = 9.6 \, \text{V}, I_{R4} = 0.096 \, \text{A} \)

Would you like more details or have any questions on this problem?

### 5 Related Questions:
1. How do you calculate the equivalent resistance of resistors in parallel?
2. What happens to the total resistance in a series circuit when you add more resistors?
3. How does the current behave in parallel circuits compared to series circuits?
4. Can you explain the significance of Ohm's law in circuit analysis?
5. What is the effect of increasing the voltage in this type of circuit?

### Tip:
In combination circuits, always simplify parallel and series connections step by step before applying Ohm's law.

Solve the following combination circuit. Redraw the circuit listing the voltages and currents for each resistor.

Learn how to solve a combination circuit with both series and parallel resistors. This problem covers key electrical concepts like Ohm's law, current, voltage, and total resistance calculation. Suitable for high school or college-level students.

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