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Earlier discussion
1 older comment kept for context.
Oluwaseun Adeyemi
From the above diagram, if each of the resistors can dissipate a maximum of 18W, the from the relation power, P = I2R, the current in the 2Ω series resistor is given by:
I2 = P/R = 18/2 = 9 => I = √9 = 3A
The effective parallel arrangement of the two 2Ω resistors: 1/R = 1/2 + 1/2 = 1Ω
∴ Total resistance in the circuit = 1 + 2 = 3Ω
current flowing the circuit = 3A
∴ Maxi. power = P = I2R = 32 x 3 = 27W