Capacitors in series and parallel

Section 1: Introduction to Capacitors

Capacitors are key electronic components that store electrical energy in an electric field.
They are unique in how they respond to DC and AC signals, with an ability to block the former while allowing the latter to pass.
They are characterised by their capacitance, measured in farads (F), which signifies their ability to store charge.

Section 2: Capacitors in Series

When capacitors are connected in series, the total capacitance (C_total) decreases.
The total capacitance for capacitors in series can be calculated using the formula: 1/C_Total = 1/C_1 + 1/C_2 + … + 1/C_n.
The effect of connecting capacitors in series is comparable to increasing the distance between the plates of a single capacitor, hence the lower total capacitance.
A series capacitor circuit’s total voltage (V_total) is the sum of the individual capacitor voltages: V_Total = V_1 + V_2 + … + V_n.

Section 3: Capacitors in Parallel

When capacitors are connected in parallel, the total capacitance increases.
Calculating the total capacitance for parallel capacitors involves simply adding up the individual capacitances: C_Total = C_1 + C_2 + … + C_n.
The voltage across each capacitor in a parallel connection is the same and equal to the supply voltage: V = V_1 = V_2 = … = V_n.

Section 4: Charging and Discharging of Capacitors

When a charging current is applied, capacitors store energy which can then be released during discharging.
The time taken for charging/discharging depends on the RC time constant, which is the product of the resistance (R) and capacitance (C) in the circuit, represented by the formula: tau = RC.
The process of charging and discharging a capacitor follows an exponential curve, understood through the equations: V = V0 * (1 – e^(-t/RC)) for charging, and V = V0 * e^(-t/RC) for discharging.

Section 5: Practical Applications of Capacitors

Capacitors play a vital role in various electronics applications, including filtering, decoupling, energy storage, and tuning in resonance circuits.
Their unique characteristics make them indispensable for creating stable power supplies, separating AC and DC components, transient suppression, and signal processing.