1. **Problem Statement:** Given a combination circuit with total voltage $V_T=20$, total current $I_T=5$, and total resistance $R_T=4$, find the individual current, voltage, and resistance for each resistor in the circuit described. 2. **Given:** - $V_T=20$ volts - $I_T=5$ amperes - $R_T=4$ ohms 3. **Circuit Description:** - Main loop resistors: $R7$ and $R9$ in series - Upper branch: $R1$ and $R2$ in series - Sub-loop between $R1$ and $R2$ contains $R4$, $R5$, and $R6$ in parallel/series - Resistor $R3$ connects the sub-loop back to the main loop 4. **Step 1: Calculate total resistance check** - Confirm $R_T = \frac{V_T}{I_T} = \frac{20}{5} = 4\Omega$ (given, consistent) 5. **Step 2: Analyze sub-loop ($R4$, $R5$, $R6$):** - Assume $R4$, $R5$, and $R6$ are connected such that $R5$ and $R6$ are in parallel, then in series with $R4$. - Equivalent resistance of $R5$ and $R6$ in parallel: $$R_{56} = \frac{R5 \times R6}{R5 + R6}$$ - Total sub-loop resistance: $$R_{sub} = R4 + R_{56}$$ 6. **Step 3: Calculate equivalent resistance of upper branch:** - $R1$ and $R2$ are in series with the sub-loop between them. - Total upper branch resistance: $$R_{upper} = R1 + R_{sub} + R2$$ 7. **Step 4: Calculate total resistance of main loop:** - $R7$ and $R9$ are in series: $$R_{bottom} = R7 + R9$$ - Total circuit resistance is parallel combination of upper branch and bottom branch: $$\frac{1}{R_T} = \frac{1}{R_{upper}} + \frac{1}{R_{bottom}}$$ 8. **Step 5: Calculate currents:** - Total current $I_T=5A$ splits between upper and bottom branches: $$I_{upper} = \frac{V_T}{R_{upper}}, \quad I_{bottom} = \frac{V_T}{R_{bottom}}$$ - Check that $I_{upper} + I_{bottom} = I_T$ 9. **Step 6: Calculate voltages and currents in each resistor:** - For series resistors, current is the same; voltage divides proportionally. - For parallel resistors, voltage is the same; current divides inversely proportional to resistance. 10. **Summary:** - Use Ohm's law $V=IR$ for each resistor. - Use series and parallel rules to find individual currents and voltages. Since exact resistor values are not given, the method above guides how to find individual currents, voltages, and resistances using the total values and circuit configuration. **Final answer:** - Use the formulas and steps above to compute individual values once resistor values are known.