Final answer:
The period of the square wave is calculated using the time constant of the RC circuit, which is 8 ms in this case. Five time constants correspond to 40 ms, which is half the period, so the full period is 80 ms. Square waves are widely used in electronics for functions like clock signals, switching power supplies, and test signals.
Step-by-step explanation:
To calculate the period of the square wave for an RC circuit, we use the time constant formula, T = RC. In this context, one time constant (represented as 1/e-×) is the time required for the voltage across the capacitor to either charge up to or discharge down to approximately 63.2% of its maximum value in an RC circuit.
The significance of 'five 1/e-×' is that the voltage will have decayed to (1/e)^5 (or approximately 0.67% of its initial value) after five time constants, which is how long the square wave should remain at a constant value before switching.
Given the resistance R = 1.00 × 10³ Ω and capacitance C = 8.00 µF, the time constant T is:
T = RC = (1.00 × 10³ Ω)(8.00 µF) = 8.00 ms
Therefore, to accommodate five time constants within one half of the square wave, we multiply the time constant by five:
Period of square wave (for one full cycle) = 2 × 5 × T = 2 × 5 × 8.00 ms = 80 ms
Square waves have a broad range of applications in electronics, including digital electronics where they serve as clock signals for synchronous systems, in switching power supplies, and as test signals in the analysis of electronic circuits and systems.