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Answer :
Final answer:
Two six ohm resistors should be connected in series, then parallel to another six ohm resistor. This will give total resistance of 9 ohms, enabling the resistors to dissipate 36 W when connected to an 18V battery.
Explanation:
In order to answer this question, we can use the formula for power P = V²/R, which is the squared voltage divided by the resistance. Given the voltage (V) is 18 V and the power (P) is 36 W, we can substitute these values into the power equation handing us the total resistance(R) required for the circuit.
So R = V²/P would give us (18)² / 36 = 9Ω. In a parallel combination of resistors, the reciprocal of the total resistance is the sum of the reciprocals of each individual resistance. Considering all the resistors are of 6 Ω , in order to have an equivalent resistance of 9 Ω, we would need to connect two 6 Ω resistors in series (which gives 12 Ω) in parallel with another one 6 Ω resistor. This gives a total resistance of 9 Ω which allows the resistors to dissipate 36 W when connected to an 18 V battery.
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