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 |
Figure 3: A series-parallel 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.
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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 = ∞.