EGN 3373 Introduction to Electrical Systems I A Systems Approach to Electrical Engineering Graphics Adapted from “Physical, Earth, and Space Science”, Tom Hsu, cpoScience.

RECALL: Whereas resistors convert electrical energy into heat, inductors and capacitors are energy storage elements. Capacitors and inductors do not generate energy. Resistors, capacitors, and inductors are all passive elements. Section 3.1 In an ideal capacitor, the stored charge, q, is proportional to the voltage between the plates.

Example q(t) = C v(t) = 1 x v(t) Section 3.1 Given this v(t) – notice units Recal dV/dt = slope of the line = [v 2 – v 1 ]/[t 2 – t 1 ]

Given the Current through a Capacitor. Find the voltage. Section 3.1 Thus, the voltage expression for the circuit symbol for capacitance is Voltage in Terms of Current

Example Section 3.1 Given this i(t) in radians; q(0) = 0 Plot i(t) => sin wave formation Then V(t) = q(t)/C

Section 3.1 Example Given a voltage waveform applied to a 10 μF capacitance. Plot current, power delivered, and energy stored from 0 to 5s.

Given the square wave current through a 0.1 μF capacitor. Find and plot the voltage, power, and stored energy. Section 3.1 Exercise

Given the square wave current through a 0.1 μF capacitor. Find and plot the voltage, power, and stored energy. Section 3.1 Exercise

Given the square wave current through a 0.1 μF capacitor. Find and plot the voltage, power, and stored energy. Section 3.1 Exercise

Section 3.2 Capacitance in Series and Parallel Capacitors in parallel Capacitors in a parallel configuration each have the same applied voltage. Their capacitances are added. Charge is apportioned among them by size.

Capacitors in series The capacitors each store instantaneous charge build-up equal to that of every other capacitor in the series. The total voltage difference from end to end is apportioned to each capacitor according to the inverse of its capacitance. The entire series acts as a capacitor smaller than any of its components. Capacitors are combined in series to achieve a higher working voltage, for example for smoothing a high voltage power supply. For example, in a pacemaker. Section 3.2 Capacitance in Series and Parallel

a) C eq = b) C eq = Exercise

RECALL Inductors An inductor's ability to store magnetic energy is measured by its inductance, in units of henries. Typically an inductor is a conducting wire shaped as a coil, the loops helping to create a strong magnetic field inside the coil due to Faraday's Law of Induction.inductancehenries Faraday's Law of Induction Section 3.4 Inductance Bar-Coil Surface Mount Thin Film Toroid Type

Section 3.4 Inductance Current in Terms of Voltage Stored Energy

Section 3.4 Inductance Note: As the current magnitude increases, power is + and stored energy accumulates; when the current is constant, the voltage is 0, thye power is 0, and the stored energy is constant; when the current magnitude falls toward 0, the power is -, showing that the energy is being returned to the other parts of the circuit. We Can Present the Same Type of Example for an Inductor

Section 3.4 Inductance Example

Section 3.5 Inductors in Series and Parallel Exercise Using KCL, write v(t) = v 1 (t) + v 2 (t) + v 3 (t) v(t) = L 1 di/dt + L 2 di/dt + L 3 di/dt then if we define L eq = L 1 + L 2 + L 3 (Add like R in series) v(t) = L eq di/dt

L eq = ? Exercise