# Cascading RC circuit w/ DC voltage. How will capacitors charging time vary?

• Agnostic
In summary, the conversation discussed the RC time constant for capacitors in a schematic and the discrepancies between theoretical and experimental calculations. It also mentioned the use of pspice and electronics work bench, as well as the use of a spark gap. The conversation concluded with the suggestion of solving the problem using a linear non-homogeneous first order differential equation.
Agnostic
In the following schematic, will the RC time constant be the same for all capacitors using the equivalent resistance of all the resistors?

When I plug it into pspice or electronics work bench, it has that the First capacitors voltage as a function of time will always be twice as much as the 10th capacitor stage as a function of time.

I just don't know...

Either way, I am only off by 5% in my theorietical and experimental calculations...just confused...

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Agnostic said:
In the following schematic, will the RC time constant be the same for all capacitors using the equivalent resistance of all the resistors?

When I plug it into pspice or electronics work bench, it has that the First capacitors voltage as a function of time will always be twice as much as the 10th capacitor stage as a function of time.

I just don't know...

Either way, I am only off by 5% in my theorietical and experimental calculations...just confused...
Does that symbol to the right mean the stages go on forever?

No, its a spark gap.

I figured it out though. A huge linear non homongenous first order differntial equation should take care of it.

Agnostic said:
No, its a spark gap.

I figured it out though. A huge linear non homongenous first order differntial equation should take care of it.

The "10" made me wonder. I think you are right about the DE. I started doing it just for 2 capacitors. Have fun

This is going to be a set of coupled differential equations isn't it?

Agnostic said:
This is going to be a set of coupled differential equations isn't it?

I should think so. The charge rate of each capacitor depends on its own charge and the charges on the adjacent capcitors. One would think the capacitor closest to the source of emf will charge faster than the next one, etc.

## 1. How does a cascading RC circuit work?

A cascading RC circuit, also known as a series RC circuit, is a circuit that consists of a resistor and capacitor connected in series with a DC voltage source. The capacitor charges and discharges through the resistor, creating a time-varying voltage across the circuit.

## 2. What is the purpose of using a capacitor in a cascading RC circuit?

The capacitor in a cascading RC circuit acts as a temporary energy storage device. It charges up when the DC voltage is applied and then discharges through the resistor, creating a time delay in the circuit. This delay can be used for various purposes, such as filtering or time-based measurements.

## 3. How does the charging time of a capacitor in a cascading RC circuit vary with DC voltage?

The charging time of a capacitor in a cascading RC circuit is directly proportional to the DC voltage applied. This means that as the DC voltage increases, the capacitor will charge faster and reach its maximum voltage in a shorter amount of time. Similarly, a lower DC voltage will result in a longer charging time for the capacitor.

## 4. What factors can affect the charging time of a capacitor in a cascading RC circuit?

The charging time of a capacitor in a cascading RC circuit can be affected by the value of the resistor and capacitor, as well as the DC voltage applied. A higher value of resistance will result in a longer charging time, while a higher capacitance will result in a shorter charging time. Additionally, any external factors such as temperature or circuit layout can also impact the charging time.

## 5. How can the charging time of a capacitor in a cascading RC circuit be calculated?

The charging time of a capacitor in a cascading RC circuit can be calculated using the formula t = RC, where t is the charging time in seconds, R is the resistance in ohms, and C is the capacitance in farads. This formula assumes that the capacitor is charging from 0% to 63.2% of its maximum voltage, which is the typical charging time used in circuit analysis.

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