Final answer:
When a dielectric is inserted into a charged capacitor that is connected to a battery, the capacitance of the capacitor increases due to the dielectric's effect on the electric field between the plates. Capacitors can be connected in series or parallel configurations, affecting the total capacitance differently.
Step-by-step explanation:
The question pertains to the concept of capacitance and what happens to a capacitor when a dielectric material is inserted into it while it remains connected to a battery. When a dielectric is inserted into a charged capacitor that is still connected to the battery, the capacitance of the capacitor generally increases. This is because the dielectric material increases the capacitor's ability to store charge without changing the voltage, as the battery maintains a constant potential difference across the plates. The insertion of a dielectric material increases the capacitance to C1 times the dielectric constant of the material (k), assuming the original capacitance is C1.
When capacitors are connected in different configurations such as in series or parallel, their equivalent capacitances can be calculated differently. In a series configuration, the equivalent capacitance is less than any individual capacitance in the series and can be found with the reciprocal sum formula 1/Ceq = 1/C1 + 1/C2 + 1/C3,... In contrast, in a parallel configuration, the total or equivalent capacitance is the sum of all individual capacitances, given as Ceq = C1 + C2 + C3,... These concepts are crucial for understanding how capacitors work in circuits and how they store and release electrical energy.