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72 lines
2.5 KiB
Python
72 lines
2.5 KiB
Python
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# source - The ARRL Handbook for Radio Communications
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# https://en.wikipedia.org/wiki/RC_time_constant
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"""
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Description
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-----------
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When a capacitor is connected with a potential source (AC or DC). It starts to charge
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at a general speed but when a resistor is connected in the circuit with in series to
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a capacitor then the capacitor charges slowly means it will take more time than usual.
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while the capacitor is being charged, the voltage is in exponential function with time.
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'resistance(ohms) * capacitance(farads)' is called RC-timeconstant which may also be
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represented as τ (tau). By using this RC-timeconstant we can find the voltage at any
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time 't' from the initiation of charging a capacitor with the help of the exponential
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function containing RC. Both at charging and discharging of a capacitor.
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"""
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from math import exp # value of exp = 2.718281828459…
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def charging_capacitor(
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source_voltage: float, # voltage in volts.
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resistance: float, # resistance in ohms.
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capacitance: float, # capacitance in farads.
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time_sec: float, # time in seconds after charging initiation of capacitor.
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) -> float:
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"""
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Find capacitor voltage at any nth second after initiating its charging.
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Examples
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--------
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>>> charging_capacitor(source_voltage=.2,resistance=.9,capacitance=8.4,time_sec=.5)
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0.013
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>>> charging_capacitor(source_voltage=2.2,resistance=3.5,capacitance=2.4,time_sec=9)
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1.446
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>>> charging_capacitor(source_voltage=15,resistance=200,capacitance=20,time_sec=2)
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0.007
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>>> charging_capacitor(20, 2000, 30*pow(10,-5), 4)
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19.975
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>>> charging_capacitor(source_voltage=0,resistance=10.0,capacitance=.30,time_sec=3)
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Traceback (most recent call last):
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...
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ValueError: Source voltage must be positive.
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>>> charging_capacitor(source_voltage=20,resistance=-2000,capacitance=30,time_sec=4)
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Traceback (most recent call last):
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...
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ValueError: Resistance must be positive.
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>>> charging_capacitor(source_voltage=30,resistance=1500,capacitance=0,time_sec=4)
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Traceback (most recent call last):
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...
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ValueError: Capacitance must be positive.
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"""
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if source_voltage <= 0:
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raise ValueError("Source voltage must be positive.")
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if resistance <= 0:
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raise ValueError("Resistance must be positive.")
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if capacitance <= 0:
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raise ValueError("Capacitance must be positive.")
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return round(source_voltage * (1 - exp(-time_sec / (resistance * capacitance))), 3)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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