Capacitors

Step 1: Understand the given information.
We are given two capacitors, each with a capacitance of . The space between the plates of one of the capacitors is filled with a dielectric material with a dielectric constant . These two capacitors are connected in series.
Step 2: Capacitance of a capacitor with dielectric.
When a dielectric material is inserted between the plates of a capacitor, the capacitance is increased by a factor of , the dielectric constant. The capacitance of the capacitor with the dielectric material is:

Step 3: Equivalent capacitance for capacitors in series.
The equivalent capacitance for two capacitors and connected in series is given by:

Where:
(capacitor without the dielectric),
(capacitor with the dielectric).
Substitute the values into the formula:


Thus:

Step 4: Conclusion.
The equivalent capacitance of the system is 10 µF, which corresponds to option (2).