Class Activity (week 7)

Charging and Discharging a Capacitor

Charging and discharging of a capacitor. Voltage in a capacitor is 90 degree lag of its current.

I = C dV(t)/dt  or V(t) = ∫I*dt + V(0).

Figure 1: Relation between The Current and Voltage of a Capacitor

Figure 2: Sinusoidal and Triangular wave input Voltage of a  Capacitor and its Current

According to the figure 2, current of a capacitor is derivative of its voltage.

Figure 3: A series-parallel circuit

When a voltage source at t = 0 connects to a empty capacitor, capacitor will act as a short circuit

(wire). Also, a completely charged capacitor acts as a open circuit.

Figure 4: Mathematical Relation of  Discharging a Capacitor

Figure 5: Schematic of Voltage an Ideal Capacitor

An Ideal capacitor keeps its voltage for a long time, but an ideal capacitor lose its voltage gradually.

Thus, an ideal capacitor is modeled similar to a capacitor parallel with a resistor. When resistance of

the resistor is equal with infinity, the capacitor is an ideal capacitor.

Figure 6: Schematic of Charging and Discharging a Capacitor

Voltage-Current Inductor Relations

         A nonideal inductor has a significant resistance, as shown in Fig. 1 because a inductor is

made of a conducting material such as copper, which has some resistance. This resistance is called 

the winding resistance (Rw), and it appears in series with the inductance of the inductor. Winding 

resistance is usually very small. A nonideal inductor also has a winding capacitance due to the

capacitive coupling (Cw) between the conducting coils. A capacitive coupling is very small and can 

be ignored in most cases, except at high frequencies. 

Figure 1: A Schematic of a non Ideal Inductor

Figure 1: Equivalent of Series- parallel Inductors

Inductor voltage difference is proportional with derivative of its current. VL(t) = L di(t)/dt ,


VL(t) = Vmax * e^(-Rt/L) , Time Constant = L/R

A inductor acts the same open circuit at t = 0s, and also it acts the same short circuit at t = ∞.