V= voltage across a resistor
I = current through the resistor
R = value of resistance.
Power dissipated by the resistor is given by : P = V²/R = I² R
I² = P / R
Each resistance dissipates energy = 18 Watts
Maximum current through B or C or A is given by : I² = 18 Watts/2 ohms
So I = 3 Amperes maximum
Since the resistances B and C are connected in parallel, the current that comes from the resistance A is divided equally between the resistance B and C.
so current through B = current through resistance C = 1/2 * current thru A
Since, the current passing thru resistor A is max = 3 ampere, then the current through resistor B and resistor C are 1.5 Amperes maximum.