Question

Derive the equation of charging and discharging of capacitor (in context of the concept of
electrostatic) when DC voltage is applied?

Answer 1

Answer on Question #82735, Physics / Electromagnetism

**Question:**

Derive the equation of charging and discharging of capacitor (in context of the concept of electrostatic) when DC voltage is applied?

**Solution:**

If an electrical circuit has resistor R, capacitor C and voltage source U, then

$$iR + \frac{q}{C} = U$$

; while current

$$i = \frac{dq}{dt}$$

. Differentiating, we obtain the desirable equation:

$$\frac{d^2 q}{dt^2} + \frac{1}{RC} \frac{dq}{dt} = 0$$

; it’s solution is well known and for the concrete case should be added by the particular solution of the inhomogeneous equation—if any—as well as to be concretized in accordance with initial and final conditions.

**The answer:**

$$\frac{d^2 q}{dt^2} + \frac{1}{RC} \frac{dq}{dt} = 0$$

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