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The image you provided shows a DC circuit with two resistors, \( R_1 = 569 \, \Omega \) and \( R_2 = 287 \, \Omega \), connected in series. The circuit has a voltage source of \( 74.31 \, V \). We are tasked with calculating the voltage, current, and power for each resistor.

### 1. Total Resistance
Since the resistors are in series, the total resistance \( R_{\text{total}} \) is the sum of \( R_1 \) and \( R_2 \):
\[
R_{\text{total}} = R_1 + R_2 = 569 \, \Omega + 287 \, \Omega = 856 \, \Omega
\]

### 2. Current in the Circuit
Using Ohm's law, the current \( I \) through the circuit can be found by dividing the total voltage by the total resistance:
\[
I = \frac{V_{\text{total}}}{R_{\text{total}}} = \frac{74.31 \, V}{856 \, \Omega} \approx 0.0868 \, A = 86.8 \, mA
\]

### 3. Voltage Across Each Resistor
The voltage drop across each resistor can be found using Ohm's law (\( V = IR \)):

- For \( R_1 \):
\[
V_1 = I \times R_1 = 0.0868 \, A \times 569 \, \Omega \approx 49.42 \, V
\]

- For \( R_2 \):
\[
V_2 = I \times R_2 = 0.0868 \, A \times 287 \, \Omega \approx 24.89 \, V
\]

### 4. Power Dissipated by Each Resistor
The power dissipated by each resistor is given by \( P = I^2 \times R \):

- For \( R_1 \):
\[
P_1 = (0.0868 \, A)^2 \times 569 \, \Omega \approx 4.27 \, W
\]

- For \( R_2 \):
\[
P_2 = (0.0868 \, A)^2 \times 287 \, \Omega \approx 2.16 \, W
\]

### Summary of Results:
- \( I = 86.8 \, mA \)
- Voltage across \( R_1 = 49.42 \, V \)
- Voltage across \( R_2 = 24.89 \, V \)
- Power dissipated by \( R_1 = 4.27 \, W \)
- Power dissipated by \( R_2 = 2.16 \, W \)

Would you like further details on any of these steps or calculations?

Here are five related questions you might explore next:
1. What is the total power dissipated in the circuit?
2. How would the current change if \( R_1 \) were doubled?
3. How would the voltage across \( R_2 \) change if the total voltage was reduced to \( 50 \, V \)?
4. What would happen to the circuit if \( R_2 \) was removed (open circuit)?
5. How does the power dissipation change if the resistors were arranged in parallel instead of series?

**Tip**: In a series circuit, the current remains the same through all components, but the voltage divides based on the resistance of each component.

Solve the DC circuit with two resistors, R1 = 569 Ω and R2 = 287 Ω, and a total voltage of 74.31 V. Find the voltage, current, and power for each resistor.

Learn how to solve a DC circuit problem with resistors R1 = 569 Ω and R2 = 287 Ω connected in series with a 74.31 V power supply. This problem covers key concepts like Ohm's law, current, voltage drop, and power dissipation across each resistor. Suitable for students in Grades 9-12.

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