A student constructs a circuit using three capacitors as shown in...

In the given circuit, the $3\ \mu\text{F}$ and $6\ \mu\text{F}$ capacitors are connected in series. Their equivalent capacitance $C_s$ is:

$C_s = \dfrac{3 \times 6}{3 + 6} = \dfrac{18}{9} = 2\ \mu\text{F}$

This combination is connected in parallel with the $2\ \mu\text{F}$ capacitor.

The effective capacitance $C_{XY}$ between terminals X and Y is:

$C_{XY} = 2\ \mu\text{F} + C_s$

$C_{XY} = 2\ \mu\text{F} + 2\ \mu\text{F} = 4\ \mu\text{F}$

Answer: $4\ \mu\text{F}$