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Chapter 2 Summary Electric Circuits and Components dq I ( t ) = -----dt current (A): V = IR ohm's law (V): R = ab ´ 10c ± tolerance (%) resistor value (W): a, b, and c Bands tol Band Color Value Color Value Black 0 Gold ±5% Brown 1 Silver ±10% Red 2 Nothing ±20% Orange 3 Yellow 4 Green 5 Blue 6 Violet 7 Gray 8 White 9 t capacitor (F): 1 V ( t ) = ---C dV I ( t ) = C -----dt Q(t) ò I ( t )dt = ---------C 0 t inductor (H): dI V ( t ) = L ----dt 1 I ( t ) = --L ò V ( t ) dt 0 N Kirchoff's Voltage Law (KVL): å Vi = 0 i=1 N Kirchoff’s Current Law (KCL): å Ii = 0 i=1 series resistors: R eq = R 1 + R 2 series capacitors: C1 C2 C eq = ----------------C1 + C2 series inductors: L eq = L 1 + L 2 series resistor voltage division: R1 - Vs , V R1 = ---------------R1 + R 2 parallel resistors 1 1 1 ------- = ----- + ----R 1 R2 R eq R2 - Vs V R2 = ---------------R 1 + R2 R1 R2 R eq = ---------------R1 + R2 parallel capacitors: C eq = C 1 + C 2 parallel inductors: L1L2 L eq = ---------------L1 + L2 parallel resistor current division: R2 - I, I 1 = ---------------R 1 + R2 R1 -I I 2 = ---------------R 1 + R2 ideal voltage source: zero output resistance, can supply infinite current. ideal current source: infinite output resistance, can supply infinite voltage. ideal voltmeter: infinite input resistance, draws no current. ideal ammeter: zero input resistance, no voltage drop. V ( t ) = V m sin ( wt + f ) ac signal: 1 w f = --- = -----T 2p frequency (Hz): phasor: V = Vm e j ( wt + f ) = V m á fñ = V m [ cos ( wt + f ) + j sin ( wt + f )] phasor relationships: r = 2 2 x +y –1 y f = tan æ --ö è xø r 1 á f 1ñ × r 2 á f 2ñ = r 1 × r 2 á f 1 + f 2ñ r 1 á f 1ñ ¤ r 2 á f 2ñ = r 1 ¤ r 2 á f 1 – f 2ñ ac Ohm’s Law with impedance: V = ZI resistor impedance: ZR = R inductor impedance: Z L = jwL = wL á 90°ñ capacitor impedance: 1 1 –j Z C = ---------- = -------- = -------- á – 90°ñ wC jwC wC power: dq dW P = -------- = V ------ = VI dt dt dc resistive power: P = VI = I 2 R = V 2 ¤ R T rms: I rms = Im 1 --- I 2 dt = -----T 2 ò 0 ac resistive power: transformer: T V rms = V 1 --- V 2 dt = ------mT 2 ò 0 P avg = V rms I rms = RI2rms = V 2rms ¤ R N V S = -----S- V P NP N I S = -----P- I P NS