V-I Relationship for a Capacitor
The voltage-current relationship for a capacitor in an electrical circuit is given by the following equation:
[Tex]i(t)=Cdv(t)/dt [/Tex]
Then,
[Tex]V = \frac{1}{j\omega C} \cdot I [/Tex]
- i(t) is the instantaneous current through the capacitor at time t.
- C is the capacitance of the capacitor.
- v (t) is the instantaneous voltage across the capacitor.
- This equation describes that the current through a capacitor is proportional to the rate of change of voltage with respect to time.
- The voltage across the terminals of a capacitor lags by current.
[Tex]V = \frac{I_m}{\omega C} \angle (\theta_i - 90^\circ)[/Tex]
Graph of V-I Relationship for a Capacitor
The graph of the V-I relationship for a capacitor is a phasor-shifted sine wave. When an AC voltage is applied, the current leads the voltage due to capacitors characteristics in the form of an electric field.
Sinusoidal Steady State Analysis – Electric circuits
In steady state (the fully charged state of the cap), current through the capacitor becomes zero. The sinusoidal steady-state analysis is a key technique in electrical engineering, specifically used to investigate how electric circuits respond to sinusoidal AC (alternating current) signals. This method simplifies the intricate details involved in time-varying AC circuits by representing voltages and currents as phasors—complex quantities that succinctly convey both amplitude and phase information.
Table of Content
- Sinusoidal Steady State Analysis
- Sinusoidal Source
- Derivation
- V-I Relation for an Inductor
- V-I Relationship for a Capacitor
- Frequency Response
- Bode Plots
- Examples