📚 How to solve electrical problems by the Laplace transform (DC Source, Question 1)
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Q. A capacitor is discharged through a resistor by throwing the switch from position 1 to position 2 at t=0. Find the current i.
Recall:
Kirchhoff's voltage law: States that the sum of the voltage that drops across a resistor (R), an inductor (L), and a capacitor (C), in an electrical circuit must be the same as the voltage source applied to that RLC circuit.
In addition, the instantaneous current in a capacitor equals the capacitance (C) times the rate of change of the voltage. Integrating this gives the voltage across a capacitor of capacitance C:
(i=C⋅dv/dt ⇒ V_c=(1/C) ∫_0^t▒i dt)
L [1]=1/( s )
L [e^at ]=1/(s−a)