Differential equation for a electric circuit

[bulbanos]

                  ___      ___
              /--|___|----|___|-\
              |        |        |
             ---      ---      ---
              -       ---      ---
              |        |        |
              \-----------------/

So I've got an AC source at the left, 2 resistors (left one 2R, right one 3R) and two capacitors with capacitance C. I need to calculate the voltage over the right capacitor with use of a differential equation. I don't know where to start to write that equation. please help

 

[saltydog]

                  ___      ___
              /--|___|----|___|-\
              |        |        |
             ---      ---      ---
              -       ---      ---
              |        |        |
              \-----------------/

So I've got an AC source at the left, 2 resistors (left one 2R, right one 3R) and two capacitors with capacitance C. I need to calculate the voltage over the right capacitor with use of a differential equation. I don't know where to start to write that equation. please help

I think you need to use Kirchoff's laws:

1. Sum of the currents into or away from any point is 0.
2. Around any closed path, the sum of the instantaneous voltage drops in a specified direction is zero.

 

[thepatientmental]

.

The differential equation for an electric circuit can be written as:

V = L di/dt + Ri + 1/C ∫i dt

where V is the voltage across the circuit, L is the inductance, R is the resistance, C is the capacitance, and i is the current flowing through the circuit. This equation is known as the Kirchhoff's voltage law and is based on the principles of conservation of energy in an electric circuit.

In your specific circuit, the voltage across the right capacitor can be calculated by considering the voltage drop across each component. The voltage drop across the AC source will be given by the amplitude of the AC voltage, while the voltage drop across the 2R resistor will be 2Ri and the voltage drop across the 3R resistor will be 3Ri. The voltage across the right capacitor will be equal to the voltage drop across the AC source minus the voltage drop across the 2R resistor and the 3R resistor.

Using this information, the differential equation for the voltage across the right capacitor can be written as:

Vc = Vsource - 2Ri - 3Ri

Substituting the values for the components in your circuit, the equation becomes:

Vc = Vsource - 5Ri

This is the differential equation for the voltage across the right capacitor in your electric circuit. To solve this equation and calculate the voltage at any given time, you will need to know the values of the AC source voltage, the resistance, and the current flowing through the circuit. You can also use this equation to analyze the behavior of the circuit and determine the effects of changing any of the components.