How does pd vary with time through a discharge of a capacitor?

I know the title is a bit obvious but the real question is :

How does pD vary with time through the discharge of a capacitor through a combination of resistors that may be in parrallel or series


E.g I'm not sure how the PD would vary through each circuit?

The pd (across the capacitor) decreases exponentially as a capacitor discharges the rate at which it decreases depends on the total resistance of the circuit. If you have resistors in series then you have a higher total resistance so that means you'll have a higher time constant (time constant=RC) and since V=V_initiale^-t/RC that means it will decrease at much slower rate as it takes a greater amount of time for the voltage to reach approx 37% of its initial value.

So if you have resistors in parallel which give a lower combined resistance which means you will have a lower time constant that'l mean the voltage across the capacitor will decrease much more quickly.

Hope this makes sense to you

So through a series the discharge is slower, got it thanks.

Nooooooo.......

The rate of discharge depends on the total resistance in the path of the discharge and not whether that current flows via a series or parallel path.

Adding resistors in series is just the sum of them where as parralel it's the 1/R equation right?

So through a series the discharge is slower, got it thanks. Is there anything else I might need to know you think?

No I understand that yes. But if there are 2 resistors in a circuit, both of say 50 ohms, one circuit set up series and the other parralel then the series circuit will discharge slower, because the total resistance is 100 ohms right compared to the parralel which is


1/r = 1/50 + 1/50 = 2/50

1/0.04 = 25 ohms so clearly the series one will discharge slower?

Well higher resistance means higher time constant so it discharges at a slower rate so it's not dependent upon series or parallel combination of resistors because if you have two small resistors in series and two massive resistors in parallel - the parallel combination even though its still has a significantly lower total resistance it may still have a bigger total resistance then the two small resistors in series.

I hope that makes things clearer for you

In the context of the situation then yes the series combination would mean the capacitor would discharge at slower rate. However, for general cases its the total resistance that determines the rate of discharge of a capacitor.