To solve the given DC circuit problem, we need to analyze the provided values and configurations of the resistors and voltages. Let's extract the relevant information from the image and work through the calculations:

Given Information:

1. Total Voltage (Vt): $85.06 \ \text{V}$
2. Total Resistance (Rt): $842.6 \ \Omega$
3. Total Current (It): $100.95 \ \text{mA}$
4. Individual Resistances:
   • $R_1 = 450 \ \Omega$
   • $R_2 = 171 \ \Omega$
   • $R_3 = 398 \ \Omega$
   • $R_4 = 273 \ \Omega$
5. Voltages and Currents through some resistors:
   • $V_{R_1} = 45.42 \ \text{V}$, $I_{R_1} = 100.95 \ \text{mA}$
   • $V_{R_4} = 27.55 \ \text{V}$, $I_{R_4} = 100.95 \ \text{mA}$

Circuit Analysis Approach:

1. Identify Series and Parallel Connections:

   • $R_1$ and $R_4$ share the same current $I_{R_1} = I_{R_4}$, indicating they are in series with the rest of the circuit.
   • $R_2$ and $R_3$ have a current of 0 mA, indicating an open circuit between them. This means no current flows through that part, and the series part with $R_1$ and $R_4$ dominates the behavior.

2. Calculate Equivalent Resistance for Series Resistors: Since $R_1$ and $R_4$ are in series: $R_{\text{series}} = R_1 + R_4 = 450 \ \Omega + 273 \ \Omega = 723 \ \Omega$

3. Verify Total Resistance Calculation: The circuit displays a total resistance of $842.6 \ \Omega$. With $R_2$ and $R_3$ having no current, it suggests they don't affect the total resistance directly. However, they might be in parallel with the series part but have an open connection, thus not contributing.

4. Check Power Calculations: Power across each resistor can be verified using $P = V \cdot I$ or $P = I^2 \cdot R$:

   • Power across $R_1$: $P_{R_1} = 45.42 \ \text{V} \times 0.10095 \ \text{A} \approx 4.58 \ \text{W}$
   • Power across $R_4$: $P_{R_4} = 27.55 \ \text{V} \times 0.10095 \ \text{A} \approx 2.78 \ \text{W}$

Conclusion:

• The primary active path involves $R_1$ and $R_4$ in series.
• The open circuit between $R_2$ and $R_3$ results in no current through that branch.
• The calculations for power and current match the given values for the resistors in the series circuit.

Would you like further details on the derivation or more explanations on series-parallel circuits? Here are 5 related questions that could deepen your understanding:

1. How do you determine if resistors are in series or parallel in a complex circuit?
2. What happens to the total current in a parallel circuit when one branch is open?
3. How can you calculate power dissipation across multiple resistors?
4. What is the significance of Kirchhoff’s Voltage Law (KVL) in analyzing circuits like this?
5. How do changes in resistance affect the overall current in a circuit?

Tip: In series circuits, the same current flows through each component, while in parallel circuits, the voltage across each component is the same.