I am a beginner at electronics so excuse my rather simplistic question.
I would like to know regarding capacitors, if a capacitor is connected in a series circuit (as shown below but with a dc supply), will it discharge?
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With a DC power supply, the capacitor will charge up to the voltage of the supply.
If you replace the DC supply with a resistor, the capacitor will discharge through the resistor until there is zero volts across the capacitor.
With an AC supply, the capacitor will continually charge and discharge as the AC voltage varies.
Since it's connected to a source of AC, it'll charge/discharge (depending on your point of reference) when the signal is one polarity and reverse when the signal changes polarity.
Charge yes. Discharge no.
If you are talking about a DC supply like a battery, the voltage across the capacitor will become the same as the supply voltage over time.
The question is how fast will this happen? This depends on the resistance in the circuit as well as the capacitance of the capacitor. You may say there is no resistance in the circuit, but there is always resistance in a real circuit.
The voltage is given by V = Vs(1 - e^(-t/RC))
V is the voltage as a function of time
Vs is the voltage of the source
e is Euler's number = 2.71828 ...
t is time in seconds
R is the resistance in ohms
C is capacitance in farads
The quantity tau = RC is called the time constant and determines how fast the capacitor will charge.
After 1 tau the capacitor will already be 63 % charged.
So it will not discharge until you remove the battery and connect it to a load like a light bulb or resistor.