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Calculation of transients in electrical circuits by the classical method

Lecture




Task 1
Calculation of transients in electrical circuits by the classical method
Build a transient when locking the key.
E = 10 V, C = 10 μF, R = 1 kΩ
τ = RC = 0.01s - the capacitor charging time constant
Uc lane = Uc mouth + Uc cv Uc mouth = E = 10 V
Calculation of transients in electrical circuits by the classical method
the transition process takes place exponentially.
τ is the time constant during which the free component of the process decreases in Calculation of transients in electrical circuits by the classical method times compared with the initial condition.

let's calculate some characteristic points:
t = τ Uc per1 = 10 (1 -1 / 2.7) = 6.3 B
t = 2τ Uc per2 = 10 (1 -1 / 7.29) = 8.63 B
t = 3 τ Uc per3 = 10 (1 -1 / 19,863) = 9.5 B
t = 4 τ Uc per4 = 10 (1 -1 / 53,14) = 9.85 B
t = 5 τ Uc per5 = 10 (1 -1 / 143,5) = 9.9 B
Calculation of transients in electrical circuits by the classical method

Task 2
Calculation of transients in electrical circuits by the classical method
Build a transition process when opening the key.
Initial conditions Uc = E = 10 V, C = 10 μF, R = 1 kΩ
τ = RC = 0.01s - the capacitor charging time constant
The time constant during which the free component of the process decreases in Calculation of transients in electrical circuits by the classical method times compared with the initial condition.

Uc per = Uc mouth + Uc cc Uc mouth = 0 V
Uc per = Uc cb = the transient process is exponentially.

let's calculate some characteristic points:
t = τ Uc per1 = 10 / 2.7 = 3.7 B
t = 2τ Uc per2 = 10 / 7.29 = 1.37 B
t = 3 τ Uc per3 = 10 / 19,863 = 0.5 B
t = 4 τ Uc per4 = 10 / 53,14 = 0.15 B
t = 5 τ Uc per5 = 10 / 143.5 = 0.1 B
Calculation of transients in electrical circuits by the classical method


Task 3
Calculation of transients in electrical circuits by the classical method
In the circuit, the inductive coil is disconnected from the DC voltage source and closed to the resistor
U = 110 V, L = 5 GN Rc = 4 Ohms, R = 6 Ohms
Find the current in the coil at t = 1 sec, it after disconnecting from the source and the voltage on R at the initial moment after switching

Solution when the source is connected to the coil (key 1 position) the current in the circuit is determined according to Ohm's law I = U / Rk = 110/4 = 27.5 A
After switching, i.e. key switching (key position 2) the electrical state of the circuit is described by the equation
Calculation of transients in electrical circuits by the classical method

Voltage UR = RI = 27.5 ∙ 6 = 165 B

Task 4
Calculation of transients in electrical circuits by the classical method

Given: E = 100 V; R1 = 20 Ohm; R2 = 30 Ohm; R3 = 10 Ohm; R4 = 40 Ohm; C = 100 μF
Determine input current Calculation of transients in electrical circuits by the classical method and write the expression Calculation of transients in electrical circuits by the classical method

Decision
1. After closing the key
We write the equation according to the laws of Kirchhoff
Calculation of transients in electrical circuits by the classical methodCalculation of transients in electrical circuits by the classical method

2. The calculation of the steady state
Uc = Us mouth + Uc cv
Calculation of transients in electrical circuits by the classical method
Equation for steady state:
Calculation of transients in electrical circuits by the classical method

3. Solve one of the methods by determining the parameters of the transient characteristics through the solution of the characteristic equation. Let's make this equation:
Calculation of transients in electrical circuits by the classical method

Replace jɷ = p where p is the root of the characteristic equation
Calculation of transients in electrical circuits by the classical method

4. When t = 0: Calculation of transients in electrical circuits by the classical method

Uc (0+) = U (R2 + R3) / (R1 + R2 + R3 + R4) = 40 B

Determine the value of A: 40 = 14.2 + AA = 25.8 B
The expression of the voltage on the capacitor takes the form: Calculation of transients in electrical circuits by the classical method
5. Write the expression for the input current. Calculation of transients in electrical circuits by the classical method
Calculation of transients in electrical circuits by the classical method
Calculation of transients in electrical circuits by the classical method
Determine the value of A: A = - 0,42
expression for input current Calculation of transients in electrical circuits by the classical method

created: 2014-09-27
updated: 2021-07-16
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Electrical Engineering, Circuit design

Terms: Electrical Engineering, Circuit design