By Paul Scherz
An intuitive, applications-driven consultant to electronics for engineers, hobbyists, and students--one that doesn't overload readers with technical element. Chock-full of illustrations--over 750 hand-drawn photographs offer transparent, exact directions on the way to flip theoretical principles into real-life contraptions. Covers built-in circuits (ICs), electronic electronics, and diverse input/output units; encompasses a entire bankruptcy at the most recent microcontrollers.
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Extra resources for Practical Electronics for Inventors
22 To find the equivalent capacitance for two capacitors in parallel, you apply Kirchhoff’s current law to the junction to the left in the circuit in this figure, which gives I = I1 + I2. 23 To find the equivalent capacitance of two capacitors in series, you apply Kirchhoff’s voltage law. 14 Reactance of a Capacitor A capacitor connected to a sinusoidal voltage source will allow displacement current to flow through it because the voltage across it is changing (recall that I = C dV/dt for a capacitor).
For this reason, other laws or theorems are needed. One set of important laws is Kirchhoff’s laws. Kirchhoff’s laws provide the most general method for analyzing circuits. These laws work for either linear or nonlinear elements, no matter how complex the circuit gets. 13 In essence, Kirchhoff’s voltage law is a statement about the conservation of energy. If an electric charge starts anywhere in a circuit and is made to go through any loop in a circuit and back to its starting point, the net change in its potential is zero.
Each form is useful in its own way; that is, sometimes it is easier to use z = a + jb, and sometimes it is easier to use either z = r(cos θ + j sin θ) or z = re jθ— it all depends on the situation. 36 Theory 33 The model shown in Fig. 36 is designed to help you get a feeling for how the various forms of a complex number are related. 2. 2 FORM OF COMPLEX NUMBER z1 = a + jb z2 = c + jd Cartesian form ADDITION/SUBTRACTION MULTIPLICATION DIVISION z1 Ϯ z2 = (a Ϯ c) + j(b Ϯ d) z1z2 = (ac − bd) + j(ad − bc) z1 ac + bd bc − ad ᎏ=ᎏ +j ᎏ z2 c2 + d2 c2 + d2 Example: Example: Example: z1 = 3 + j4, z2 = 5 − j7 z1 = 5 + j2, z2 = −4 + j3 z1 = 1 + j, z2 = 3 + 2j z1 + z2 = (3 + 5) + j(4 − 7) = 8 − j3 z1z2 = [5(−4) − 2(3)] + j[5(3) + 2(−4)] = −26 + j7 z1 1(3) + 1(2) 1(3) − 1(2) ᎏ = ᎏᎏ + j ᎏᎏ z2 32 + 22 32 + 22 5 1 = ᎏ + jᎏ 13 15 z1 = cos θ1 + j sin θ1 z2 = cos θ2 + j sin θ2 Polar form (trigonometric) z1 = r1eθ1 z2 = r2eθ2 Polar form (exponential) Can be done but involves using trigonometric identities; it is easier to convert this form into the Cartesian form and then add or subtract.