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 \(V = i\,R\) \( \Rightarrow \) \(10.5 = 2 \times R\) \( \Rightarrow \)  \(R = \frac{{21}}{4}\,\Omega \)