Which equation best expresses the time constant in a electrical circuit?

The time constant in an electrical circuit, particularly in circuits involving resistors and capacitors (RC circuits), is best expressed by the equation TC = C x R. In this context, TC represents the time constant, C represents the capacitance measured in farads, and R represents the resistance measured in ohms.

The time constant indicates the time it takes for the voltage across the capacitor to charge to approximately 63.2% of its maximum value during a charging process, or to discharge to about 36.8% of its initial value during a discharging process. This relationship is foundational in understanding how quickly a capacitor responds to changes in voltage in the circuit, allowing for the analysis of transient responses in electrical engineering and related fields.

The other options present alternative formulations that do not correctly represent the time constant. For example, dividing resistance by capacitance or adding/subtracting capacitance and resistance does not relate to the exponential charge and discharge behavior governed by RC time constants. Understanding this equation is critical for anyone working with electrical circuits, particularly in applications involving timing, filtering, and signal processing.