Final answer:
To achieve time constants from 2.00 to 15.0 seconds using a 0.500-µF capacitor, the resistor in the RC circuit must vary within a calculated range. This resistor variation allows the timing device in an automobile's wiper system to adjust the time intervals accordingly.
Step-by-step explanation:
Understanding RC Circuits and Time Constants
The question relates to the design of a timing device in an automobile's intermittent wiper system, which is based on an RC time constant. An RC circuit typically includes a resistor (R) and a capacitor (C), and the time constant (τ) for the circuit is given by the product of R and C (τ = R * C). To determine the range over which the resistor must vary to achieve time constants from 2.00 to 15.0 seconds with a 0.500-µF capacitor, we use the formula and solve for R, given that the capacitor value is fixed.
To find the minimum value of R for a 2.00-second time constant, we rearrange the formula to R = τ / C and substitute the values giving us R = 2.00 s / 0.500 µF. Likewise, for the maximum value of R for a 15.0-second time constant, we use the same process. As a result, the resistor must range between these calculated minimum and maximum values to provide the desired time constants in the wiper system. This application demonstrates how electronics incorporate RC circuits to control the timing of various functions, such as in a 555 timer which provides timed voltage pulses controlled by an RC circuit.
In the context of electronics and timers, small and large time intervals are typically expressed in seconds and can be scaled using appropriate prefixes, such as microseconds (µ3 × 10-6 s) or megaseconds (5 × 106 s), providing a range of time bases for. This versatility allows for precise control over timing in a multitude of applications.