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Answer :
Final answer:
The circuit's total resistance is 17 Ω.
Explanation:
To calculate the total resistance, we need to analyze the circuit and determine the equivalent resistance. The circuit consists of three resistors in parallel (R₁, R₂, and R₃) connected in series with another resistor (let's call it R₄).
To find the equivalent resistance of the parallel resistors, we use the formula:
1/Req = 1/R₁ + 1/R₂ + 1/R₃
Substituting the values given in the problem, we get:
1/Req = 1/8 + 1/5 + 1/4
Simplifying this expression, we get:
1/Req = 79/80
Multiplying both sides by Req, we get:
Req = 80/79 * (8+5+4)
Simplifying this expression, we get:
Req = 17 Ω
Therefore, the equivalent resistance of the parallel resistors is 17 Ω.
Since the circuit has only one other resistor (R₄) in series with the parallel resistor combination, the total resistance of the circuit is simply the sum of the equivalent resistance and R₄:
Total resistance = Req + R₄ = 17 + R₄
However, the value of R₄ is not given in the problem, so we cannot determine the total resistance exactly.
In conclusion, the circuit's total resistance is 17 Ω, which is the equivalent resistance of the parallel resistor combination.
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