Electrical circuit is built with:
• voltage source E
• resistor R
• switches X1, X2
• inductivity L
Switch X2 is being closed and switch X1 is being opened, both switches change their state in the same time. As a result inductivity discharging current i(t) starts to flow in circuit. Immediately after closing the switch X2 the transient state occurs in electrical circuit, therefore, commutation principles have to taken under consideration. Kirchhoff's voltage law equation will be written for circuit. General formula for inductivity's voltage will be taken under consideration.
Kirchhoff's voltage law equation will be rewritten to create differential equation.
Differential equation with separated variables which has to be solved. To solve this differential equation substitution method will be applied.
After solving differential equation a relation for inductivity's current iL(t) is obtained. Formula is related to inductivity discharging time's transient state. Inductivity discharging circuit's time constant appears in formula → T=L/R.
To obtain formula for inductivity's voltage uL(t) a derivative of inductivity's current has to be computed → uL(t)=L·diL(t)/dt. Formula is related to inductivity discharging time's transient state. Inductivity discharging circuit's time constant appears in formula → T=L/R.
Inductivity's discharging current iL(t) received from simulation for following elements values:
• voltage source E=12V
• resistor R=1kΩ
• inductivity L=1mH
Inductivity's discharging voltage uL(t) received from simulation for following elements values:
• voltage source E=12V
• resistor R=1kΩ
• inductivity L=1mH
