The current in a capacitor is [tex]i = C\frac{dv}{dt}[/tex] and the voltage in an inductor is [tex]v = L\frac{di}{dt}[/tex].Corneo said:I have been taught that the voltage in a capacitor and the current in an inductor cannot change instanteously. This is important especially when solving differential equations for a circuit network. Can someone explain to me why these events cannot happen? To the extent of my knowledge for these events to happen, there is a need of infinite energy.
Yes, the delta 'function' or impulse, is a signal with infinite amplitude and zero duration. Because of this it has finite energy. So a current impulse can instantaneously change the voltage of a capacitor and a voltage impulse can instantaneously change the current in an inductor.EvLer said:he-he...
we were just told last week in lecture that capacitor charge (or voltage) CAN change instantaneously if input signal is delta function.
You are right. Delta function is an artificial construct that allows us to solve for the current fed to an ideal capacitor, initially discharged, connected to an ideal voltage source of V volts. According to Kirchoff's voltage law, the voltage in the capacitor rises instantaneously from 0 to V volts. This is only possible if the current charging the capacitor is [tex]i_C(t) = CV\cdot\delta(t)[/tex].chroot said:Of course, delta functions don't exist in the real world. There's no such thing as an impulse with infinite amplitude and zero duration in the real world.
- Warren
EvLer said:he-he...
we were just told last week in lecture that capacitor charge (or voltage) CAN change instantaneously if input signal is delta function.
A capacitor voltage is the potential difference between the two plates of a capacitor. It works by storing electrical energy in an electric field between the plates. When a voltage is applied, one plate becomes positively charged and the other becomes negatively charged, creating an electric field between them. The capacitor can then release this stored energy when needed.
The voltage across a capacitor is directly proportional to the amount of charge stored. This relationship is described by the equation V = Q/C, where V is the voltage, Q is the charge, and C is the capacitance of the capacitor. This means that as the amount of charge stored increases, the voltage across the capacitor also increases.
Inductor current is the flow of electric charge through an inductor. It behaves in a circuit by resisting changes in current, either by storing or releasing energy. When a current is first applied to an inductor, it resists the change and builds up a magnetic field. As the current continues to flow, the inductor will eventually reach a steady state where the current remains constant.
The current through an inductor changes with time according to the equation I = I0e-t/τ, where I is the current at any given time, I0 is the initial current, t is time, and τ is the time constant of the inductor. This means that the current will decrease over time, eventually reaching zero as the inductor reaches a steady state.
In an AC circuit, the capacitor voltage and inductor current are out of phase with each other. This means that as the voltage across the capacitor is increasing, the current through the inductor is decreasing, and vice versa. This relationship is described by the equation VC = -L(dI/dt), where VC is the capacitor voltage, L is the inductance, and dI/dt is the rate of change of the inductor current.