Electrical circuit is built with:
• voltage source E
• resistor R
• switch X1
• capacitor C
Capacitor has collected an initial charge Q0 between its electrodes, thus, it has an initial voltage UC0=Q0/C.
Switch X1 is being closed at specific time, thus, current i(t) starts to flow in circuit. Immediately after closing the switch X1 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 capacitor's current 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 capacitor's voltage uC(t) is obtained. Formula is related to capacitor charging time's transient state. Capacitor charging circuit's time constant appears in formula → T=R·C.
To obtain formula for capacitor's current iC(t) a derivative of capacitor's voltage has to be computed → iC(t)=C·duC(t)/dt. Formula is related to capacitor charging time's transient state. Capacitor charging circuit's time constant appears in formula → T=R·C.
Capacitor's charging voltage uC(t) received from simulation for following elements values:
• voltage source E=12V
• resistor R=1kΩ
• capacitor C=1μF
Capacitor has ability to store energy in electric field.
Capacitor's charging current iC(t) received from simulation for following elements values:
• voltage source E=12V
• resistor R=1kΩ
• capacitor C=1μF
Capacitor has ability to store energy in electric field.
