A resistor and a capacitor areconnected in series to an emf...

A resistor and a capacitor areconnected in series to an emf source. The time constant for the circuit is 0.870 $\mathrm{s}$ . (a) A second capacitor, identical to the first, is added in series. What is the time constant for this new circuit? (b) In the original circuit a second capacitor, identical to the first, is con- nected in parallel with the first capacitor. What is the time constant for this new circuit?

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Key Concepts

RC Circuit

An RC circuit is an electrical circuit composed of a resistor (R) and a capacitor (C) connected to a voltage source. In such circuits, the capacitor charges and discharges through the resistor, and the voltage across the capacitor changes exponentially over time. This behavior is central to timing and filtering applications in electronics.

Time Constant

The time constant, denoted by ?, is defined as the product of the resistance (R) and the capacitance (C) in an RC circuit (i.e., ? = RC). It provides a measure of the speed at which the capacitor charges or discharges, with a larger time constant indicating a slower rate of change. Approximately 63% of the full voltage is reached after one time constant during charging.

Equivalent Capacitance

When capacitors are connected in a circuit, their effective capacitance depends on whether they are arranged in series or parallel. For capacitors in series, the total (equivalent) capacitance is less than any individual capacitance and is calculated by the reciprocal formula, while for capacitors in parallel, the capacitances add directly, resulting in a larger equivalent capacitance. This concept is essential for understanding how circuit modifications impact overall behavior such as the time constant.

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