Energy stored in a capacitor — common mistakes

When calculating energy, always ensure your capacitance is in Farads (F) and voltage in Volts (V). Be careful with units like microfarads ($\mu F$) – convert them to Farads by multiplying by $10^{-6}$.

The voltage across a capacitor isn't constant during charging. It starts from zero and increases to V. The $\frac{1}{2}$ factor accounts for this average voltage, representing the area of a triangle under the Q-V graph, which is how we calculate the total work done to charge it.

The time constant ($\tau = RC$) provides a critical measure of how quickly a capacitor charges or discharges. It's the time required for the charge, voltage, or current to fall to approximately 37% of its initial value, giving insight into the circuit's transient response.

In an ideal scenario, yes. However, in reality, all capacitors have some internal leakage resistance, meaning the charge will slowly dissipate over time, even if disconnected from a circuit. This self-discharge can be very slow but is not truly indefinite.