Given,
Battery emf (ε) = 12 V
Voltage rating of each bulb (V) = 12 V
Power rating of each bulb (P) = 18 W
(a) 1. Let the resistance of each bulb be R.
Then, \mathrm{P}=\frac{\mathrm{V}^2}{\mathrm{R}}
⇒ \mathrm{R}=\frac{\mathrm{V}^2}{\mathrm{P}}=\frac{12^2}{18}=\frac{144}{18}
⇒ R = 8 Ω
2. Since B2 and B3 are connected in parallel:
\frac{1}{\mathrm{R_P}}=\frac{1}{\mathrm{R_1}}+\frac{1}{\mathrm{R_2}}
Here, R1 = R2 = 8 Ω
⇒ \frac{1}{\mathrm{R_P}}=\frac{1}{8}+\frac{1}{8}=\frac{2}{8}
⇒ RP = 4 Ω
This parallel combination is in series with B1.
Total resistance, RS = RP + R = 4 + 8 = 12 Ω
Therefore,
Current drawn = \frac{\text{Battery emf}}{\text{Total resistance}}=\frac{12}{12} = 1 A
Hence, the current drawn from the battery is 1 A.
(b) When B3 is removed, B1 and B2 remain in series.

Equivalent resistance = 8 + 8 = 16 Ω
Since the resistance increases, the current in the circuit decreases.
Hence, the brightness of B1 decreases.