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In the parallel connected circuit, two 6V 3W lamps are connected in parallel in order to consume a total power of 6W from the 6V supply. Once again, the current flowing in each lamp can be calculated from:
I = P/V = 6W/3V = 0.5A
Note that the total current delivered by the battery must be twice this value, or 1A.
Applying Ohm's Law to determine the working resistance of each lamp (i.e. the resistance when illuminated) gives:
R = V/I = 6V/0.5A = 12Ω
Since the circuit demands a total current of 1A (i.e. 0.5A + 0.5A), the effective resistance of the circuit must once again be 6Ω.
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