advertisement

Physics 331 Test 3 Formula Sheet Capacitors and Capacitance Q C= [F] (Farads) V Capacitors in Series: 1 1 1 1 ..... C T C1 C 2 C 3 Capacitors in Parallel: C T C1 C 2 C 3 ..... Charging a Capacitor: t i(t) E - RC e R v R ( t) E e - t RC v C ( t) E(1 - e - t RC = RC ) Discharging a Capacitor: t i(t) Vo - e R v R ( t) Vo e - t - t v C ( t) Vo e ' = RTC Energy Stored in a Capacitor W= Q2 1 1 C V2 Q V 2C 2 2 Inductors and Inductance di VL = L dt Inductors in Series: LT = L1 + L2 + L3 +. . . . Inductor in Parallel: 1 1 1 1 ..... L T L1 L 2 L 3 Current build up (switch initially closed after having been opened) At v L ( t) E e - t t v R ( t) E(1 - e ) i(t) E R (1 e - t ) = Current decay (switch moved to a new position) - t i(t) I o e vR(t) = R i(t) vL(t) = RT i(t) Energy Stored in an Inductor W= 1 2 LI 2 ' = L RT L R =2f f = 1/T Complex Numbers: M a 2 b2 polar form: Alternating Current C = M cos + j M sin C = a + j b: b tan -1 a C=M Inductive Reactance: Resistance |XL| = L R Impedance: ZR = R 0 Inductance: ZC = XC -90 = 1 / (C) -90 Resistance: Capacitance: Capacitve Reactance: Ohm’s Law for AC: V=IZ Components in Series: ZT = Z1 + Z2 + Z3 + . . . |XC| = 1 / ( C) ZL = XL 90 = L 90 Time Domain: v(t) = Vm sin ( t ) Phasor Notation: V = Vrms (books notation) I = Irms V = Vm (also acceptable) I = Im Vrms = Vm/2 i(t) = Im sin ( t ) Irms = Im/2 Ohm’s Law V = I R Power dissipated in a resistor in the form of heat P=VI=I2R=V2/R Resistors in Series RT = R1 + R2 + R3 + . . . Kirchhoff’s Voltage Law: The sum of the voltage drops around any closed loop equals the sum of the voltage rises around that loop. Vrise Vdrop (around any closed loop) Rx RT Voltage Divider Law: Vx V Resistors in Parallel: 1 1 1 1 ... R T R1 R 2 R 3 Kirchhoff’s Current Law: The sum of all current entering a junction, or any portion of a circuit, equals the sum of the current leaving the same. Ienter Iexit (any junction) Current Divider Rule: I x I RT Rx