A 2.00- and a 7.50-μF capacitor can be connected in series...

A $2.00-$ and a $7.50-\mu \mathrm{F}$ capacitor can be connected in series or parallel, as can a 25.0 - and a $100-\mathrm{k} \Omega$ resistor. Calculate the four $R C$ time constants possible from connecting the resulting capacitance and resistance in series.

Key Concepts

Capacitors in Series and Parallel

Capacitors can be connected in series or parallel, and the method of connection affects the overall (or equivalent) capacitance of the network. In a parallel configuration, the equivalent capacitance is simply the sum of the individual capacitances, which increases the overall charge storage capacity. In a series configuration, however, the reciprocals of the capacitances add together, yielding an equivalent capacitance that is lower than any individual capacitor’s capacitance. Understanding this is essential for designing circuits with precise timing or filtering characteristics.

Resistors in Series and Parallel

Resistors can also be arranged in series or parallel, which changes the net resistance of the circuit. When resistors are connected in series, their resistances add directly, leading to a higher total resistance. Conversely, when they are connected in parallel, the total resistance is found by taking the reciprocal of the sum of the reciprocals of the individual resistances, resulting in a lower overall resistance. This knowledge is vital for controlling current flow and voltage drops in various parts of a circuit.

RC Time Constant

The RC time constant, denoted as ?, is a fundamental property of RC circuits, calculated as the product of resistance (R) and capacitance (C). It characterizes the rate at which a capacitor charges or discharges through a resistor and dictates the transient response of the circuit. The concept of the RC time constant is key in applications ranging from filtering signals to timing circuits, as it provides a quantifiable measure of the circuit’s dynamic behavior.

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