b
For normal brightness of each bulb see following circuit. Current through each bulb $=$ $0.5\, A$
So main current $i = 2\,A$
Also, voltage across the combination $ = 1.5\,V$
So voltage across the resistance $ = 10.5\,V$
Hence for resistance $V = i\,R$ $ \Rightarrow $ $10.5 = 2 \times R$ $ \Rightarrow $ $R = \frac{{21}}{4}\,\Omega $
