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Theoretical foundations of electrical engineering

Transient processes of the first order, solution example

Given
E0=100 V;
a·τ=2;
L=2 mH=0,02 H;
C=10 μF=10-5 F;
R1=1 ohm;
R2=4 ohms;
R3=1 ohm.

Find
uC(t)-?(numerically and diagram);

Solution

Transient processes of the first order
Find characteristic resistance of the circuit p, for this purpose we equate to zero the input resistance:
Calculation of Transient processes of the first order
Circuit time constant:
Calculation of Transient processes of the first order
Find steady voltage across the capacitor. At constant value of electromotive force the capacitor is equal to the break – therefore, current does not flow in the circuit: uC уст=E;
Find the voltage value across the capacitor before switching. The circuit is open, there are no energy sources in it , therefore, all voltage drops on elements are equal to zero: uC(0-)=uC(0)=0;
General solution for voltage across the capacitor can be written in the form:

Find constant of integration A from the initial conditions:

All unknown are defined, it is possible to write the answer:

Find the limit of the diagram construction:
max=4τ=4·2·10-5=8·10-5 с=80 мкс;

The dotted line showed electromotive force value in the circuit.
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