Final answer:
After two time constants, the voltage on an initially uncharged capacitor charged through a resistance will be approximately 86.5% of the final voltage. Capacitors should be used within a specified percentage tolerance of their labeled rating for proper function and safety.
Step-by-step explanation:
The question pertains to the operation and characteristics of capacitors in electrical circuitry. Specifically, after two time constants in an RC circuit (where R is resistance and C is capacitance), the voltage across a capacitor will reach approximately 86.5% of its final value if it started charging from an initially uncharged state. This is derived from the formula for charging a capacitor through a resistor, V = Vfinal(1 - e-t/RC), where Vfinal is the maximum voltage (emf), t is the time, and e is the base of the natural logarithm. Given that one time constant (τ) is equal to the product of the resistance and the capacitance (RC), after two time constants (or 2τ), the formula simplifies to (1 - e-2), which gives approximately 86.5%.
Capacitors must also be used within certain tolerances, typically expressed as the capacitor must be within __% of the rating on the label. This is to ensure that the capacitor operates correctly within a given electrical circuit, adhering to manufacturers' specifications for safety and functionality.