In theory, a capacitor can be discharged instantly, but in practical scenarios, several factors affect the discharge rate. The discharge of a capacitor is essentially an RC circuit phenomenon, where 'R' is the resistance through which it discharges and 'C' is its capacitance. The time constant (τ) for a capacitor's discharge is given by τ = RC, indicating the time it takes for the voltage across the capacitor to drop to about 37% of its initial value. In reality, factors like the internal resistance of the capacitor, the resistance of the circuit it's discharging through, and inductance in the circuit all contribute to preventing an instantaneous discharge. Thus, while theoretically conceivable, an instantaneous discharge is practically unachievable due to these inherent electrical properties and limitations.

Connecting capacitors in parallel versus in series significantly affects the total energy stored. In a parallel configuration, the capacitors have the same voltage across each of them as the source. The total capacitance in a parallel arrangement is the sum of the individual capacitances, leading to increased overall energy storage according to the formula W = 1/2 CV². In contrast, when capacitors are connected in series, the total capacitance decreases (the reciprocal of the total capacitance is the sum of the reciprocals of individual capacitances). The voltage divides among the capacitors, reducing the energy stored in each. Consequently, for the same total voltage and identical capacitors, a parallel arrangement stores more energy than a series arrangement.

The dielectric material in a capacitor significantly affects its energy storage capacity. The dielectric material enhances a capacitor's ability to store charge, thereby increasing its capacitance. The capacitance of a capacitor is directly proportional to the permittivity of the dielectric material. A material with a higher permittivity allows the capacitor to store more charge at the same voltage, leading to increased energy storage, as evident from the formula W = 1/2 CV². Additionally, different dielectric materials have varying dielectric strengths, determining the maximum voltage the capacitor can withstand before breaking down, which in turn affects the maximum energy it can store.

The energy stored in a capacitor cannot be negative. The formulae for calculating the energy stored in a capacitor, W = 1/2 QV or W = 1/2 CV², both involve squared terms or products of quantities that are always positive or zero. Since voltage (V), charge (Q), and capacitance (C) are always non-negative in a physical context, the energy calculated from these formulae will also be non-negative. The concept of negative energy storage in a capacitor does not align with physical laws, as it implies a scenario where the capacitor would be releasing more energy than it has received or stored, which is not possible under the conservation of energy principle.

The energy stored in a capacitor being proportional to the square of the voltage is a consequence of how energy is built up in the capacitor. When charging a capacitor, each incremental addition of charge requires slightly more work than the last because it is done against an increasing electric potential (voltage). Mathematically, this relationship is captured in the integral of the voltage with respect to charge, leading to the formula W = 1/2 CV². The squaring of the voltage in this formula reflects the quadratic nature of energy accumulation in the capacitor: as the voltage doubles, the energy stored increases by a factor of four, demonstrating the square relationship.