A student is given three identical capacitors, each having a...

Using three identical capacitors of capacitance $C$, there are exactly four possible configurations that use all three components:

1. All three in series:
$C_{eq} = \dfrac{C}{3}$

2. All three in parallel:
$C_{eq} = C + C + C = 3C$

3. Two in series, connected in parallel with the third:
$C_{eq} = \dfrac{C}{2} + C = \dfrac{3C}{2}$

4. Two in parallel, connected in series with the third:
$C_{eq} = \dfrac{(2C \times C)}{2C + C} = \dfrac{2C}{3}$

Comparing these valid results with the given options, $\dfrac{4C}{3}$ is not a possible equivalent capacitance.

Answer: $\dfrac{4C}{3}$