Let's review the presented solution step by step and verify whether the calculations and logic are correct. There seems to be a mistake, so I will make corrections where necessary.
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Incorrect Assumption for R:
- You assumed the unknown resistor R is 8Ω without any justification. It would be better to keep it as an unknown and move forward unless more information is provided.
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Equivalent Resistance Calculation:
- The formula used for calculating equivalent resistance \( R_{eq} \) is correct: \[ \frac{1}{R_{eq}} = \frac{1}{8} + \frac{1}{R} \]
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Total Resistance Calculation:
- The total resistance calculation currently incorrectly states that "20Ω resistor" is included. According to your description, there is a 2Ω resistor in series with the parallel resistors. The correct formulation should be: \[ R_{total} = 2 + R_{eq} \]
- If you substitute \( R_{eq} \) with \( 4Ω \) (assuming \( R = 8Ω \)), then: \[ R_{total} = 2 + 4 = 6Ω \]
- So \( R_{total} \) is not 24Ω.
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Current Calculation:
- With the correct total resistance: \[ I = \frac{V}{R_{total}} = \frac{24V}{6Ω} = 4A \] This is different from your assumed value of 1A.
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Voltage Calculation across the Parallel Combination (V2):
- The voltage across the 2Ω resistor can be calculated: \[ V_{2Ω} = I \cdot 2Ω = 4A \cdot 2Ω = 8V \]
- Thus, \( V2 \) across the parallel resistors is: \[ V2 = 24V - 8V = 16V \]
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Current through the 8Ω Resistor:
- The total voltage across the parallel resistors is \( 16V \) (as found in the previous step).
- The current through the 8Ω resistor is given by: \[ I_{8Ω} = \frac{V2}{8Ω} = \frac{16V}{8Ω} = 2A \]
- Thus, your current assumption of \( 0.5A \) is incorrect.
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Power Dissipation on the 8Ω Resistor:
- Using the previously calculated current \( I_{8Ω} \): \[ P = I^2 \cdot R = (2A)^2 \cdot 8Ω = 4 \cdot 8 = 32W \]
Conclusion Revised:
- Equivalent Resistance \( R_{eq} \): This would have to remain \( \frac{1}{R_{eq}} = \frac{1}{8} + \frac{1}{R} \) until R is defined.
- Total Resistance \( R_{total} \): 6Ω with the assumption that the unknown resistor is 8Ω.
- Reading on V1: 24V remains correct.
- Reading on V2: Corrected to 16V.
- Reading on A1: Corrected to 4A.
- Power on the 8Ω Resistor: Corrected to 32W.
Your original solution has several crucial errors in the assumptions and calculations. It is important to clarify values upfront and ensure calculations reflect the logical flow of working with circuits.