DC Capacitor Calculations: Charging, Discharging and Time Constants in RC Circuits

The video provides a practical introduction to capacitors in DC circuits, differentiating polarized electrolytic capacitors from non-polar ceramic types, and showing how charging and discharging occur, both in parallel and series configurations, and how to compute charge, energy, and time constants in RC circuits.

It explains how a capacitor charges when connected to a battery through a resistor, why a resistor is often used to control charging time, and how to analyze total capacitance in parallel and in series. The content also discusses energy storage, symbol conventions, and the exponential nature of RC charging and discharging curves, including voltage behavior across capacitors and loads such as a lamp.

Introduction

The video introduces capacitors as essential components in DC circuits and presents two common types: polarized electrolytic capacitors and non-polar ceramic capacitors. It explains how polarity matters for electrolytics, how ceramic capacitors can generally be connected either way, and how symbols depict polarization. The narrator emphasizes that capacitors store charge and create voltage differences between plates due to the insulating dielectric between them.

Capacitor Basics and Symbols

Key concepts include the relationship between charge, capacitance, and voltage, expressed as Q = C × V. The video walks through a practical example: a 12 V, 100 μF capacitor stores Q = 0.0012 C, and, if needed, the required capacitance to store a given charge at a fixed voltage can be calculated as C = Q / V. It also introduces energy storage in a capacitor, E = 0.5 × C × V², and demonstrates how to compute energy for a 100 μF capacitor charged to 12 V.

Charging and Discharging in DC Circuits

When a capacitor is connected to a DC source, the battery drives charge onto one plate and away from the other, until the capacitor voltage matches the source. Electrons do not pass through the dielectric; instead, the capacitor charges and stores energy. Discharging occurs when a path is provided, such as a switch or a lamp, allowing current to flow as the capacitor voltage drops.

Capacitors in Parallel and Series

In parallel, capacitors act as a single larger capacitor, with total capacitance CT = ΣCi. The charge stored is Qtotal = CT × V, where V is the supply voltage. The video provides examples showing how two capacitors, 10 μF and 220 μF, combine to 230 μF in parallel. In series, the total capacitance CT is found via 1/CT = Σ(1/Ci). The series combination always yields a CT smaller than the smallest individual capacitor, and each capacitor can hold a different voltage, even though the charge on each is the same in a series chain. The narrator demonstrates a three-capacitor series example and discusses how to determine individual voltages from Q = C × V.

Practical Examples: Lamps and Filtering

Placing a capacitor in parallel with a lamp lets the capacitor power the lamp after the main supply is removed, with brightness fading as the capacitor discharges. Conversely, placing capacitors in series with a lamp shows the lamp lighting briefly and then turning off as the capacitor voltage approaches the supply. The video also discusses how multiple capacitors can be added to reach a desired total capacitance for high-current or low-noise applications, illustrating the utility of capacitors in filtering and supply smoothing.

Time Constants and RC Circuits

A central concept is the RC time constant τ = R × C, which governs how quickly a capacitor charges or discharges through a resistor. The video walks through calculations using 10 kΩ and 0.0001 F to yield a 1 s time constant, and explains how the voltage across the capacitor follows an exponential curve during charging and discharging. It presents a sequence of approximate voltage levels at each time constant (63.2%, 86.5%, 95%, 98.2%, and 99.3% of the final voltage for charging) and discusses how many time constants are needed to reach near full voltage. Discharging behavior is shown with complementary percentages (36.8%, 13.5%, 5%, 1.8%, 0.7%), warning that the voltage never truly reaches zero in a real RC circuit.

Key Takeaways and Practice

The video emphasizes the importance of recognizing that current in a series RC circuit decreases as the capacitor voltage increases, and that once the capacitor reaches full voltage, no current flows. In contrast, a lamp in a circuit with a direct connection would rapidly reach full brightness and then fade differently as the capacitor charges. The exponential nature of charging and discharging is highlighted, along with the practical use of time constants to estimate response times in RC networks. The closing segments encourage further exploration of electronic circuits and point viewers toward additional learning resources.