a8:T899,

2I_0/\pi \approx 0.637\,I_0

72:["$","span","code-0",{"className":"SmxAaG_mathInline SmxAaG_mathInlineScroll","data-math":"inline","tabIndex":0,"dangerouslySetInnerHTML":{"__html":"$a8"}}] 73:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"rms value of a sinusoidal current?"}]]}] a9:Td0b,

I_0/\sqrt2 \approx 0.707\,I_0

74:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline SmxAaG_mathInlineScroll","data-math":"inline","tabIndex":0,"dangerouslySetInnerHTML":{"__html":"$a9"}}],"."]}]]}] 75:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"What does an AC voltmeter on the mains read?"}]]}] 76:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"The rms value, 230 V (peak about 325 V)."}]]}] 77:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Phase relation in a pure resistor?"}]]}] 78:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Current in phase with voltage."}]]}] 79:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Phase relation in a pure inductor?"}]]}] 7a:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Current lags the voltage by 90° (π/2)."}]]}] 7b:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Phase relation in a pure capacitor?"}]]}] 7c:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Current leads the voltage by 90° (π/2)."}]]}] 7d:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Inductive reactance?"}]]}] aa:T77a,

X_L = \omega L = 2\pi fL

7e:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline","data-math":"inline","tabIndex":"$undefined","dangerouslySetInnerHTML":{"__html":"$aa"}}]," (ohm)."]}]]}] 7f:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Capacitive reactance?"}]]}] ab:T952,

X_C = 1/(\omega C) = 1/(2\pi fC)

80:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline SmxAaG_mathInlineScroll","data-math":"inline","tabIndex":0,"dangerouslySetInnerHTML":{"__html":"$ab"}}]," (ohm)."]}]]}] 81:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Shape of the X_L and X_C graphs against f?"}]]}] 82:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"X_L: straight line through the origin. X_C: rectangular hyperbola."}]]}] 83:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Why does a capacitor block steady DC?"}]]}] 84:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"For f = 0, X_C = 1/(2πfC) is infinite."}]]}] 85:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Impedance of a series LCR circuit?"}]]}] ac:T11cf,

Z = \sqrt{R^2 + (X_L - X_C)^2}

86:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline SmxAaG_mathInlineScroll","data-math":"inline","tabIndex":0,"dangerouslySetInnerHTML":{"__html":"$ac"}}],"."]}]]}] 87:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Phase angle of a series LCR circuit?"}]]}] ad:Ta43,

\tan\phi = (X_L - X_C)/R

88:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline","data-math":"inline","tabIndex":"$undefined","dangerouslySetInnerHTML":{"__html":"$ad"}}],"."]}]]}] 89:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Series RC circuit: does the current lead or lag?"}]]}] 8a:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Leads, by an angle between 0° and 90°; tan φ = 1/(ωCR)."}]]}] 8b:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Voltmeters read V_R = 30 V and V_L = 40 V in a series RL circuit. Supply voltage?"}]]}] 8c:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"50 V (phasor sum, not 70 V)."}]]}] 8d:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Average power in an AC circuit?"}]]}] ae:T8ef,

P = V_\text{rms}I_\text{rms}\cos\phi

8e:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline SmxAaG_mathInlineScroll","data-math":"inline","tabIndex":0,"dangerouslySetInnerHTML":{"__html":"$ae"}}],"."]}]]}] 8f:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Power factor of a series LCR circuit?"}]]}] 90:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline","data-math":"inline","tabIndex":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\cos\\phi = R/Z

"}}],"."]}]]}] 91:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Power taken by an ideal inductor or capacitor?"}]]}] 92:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Zero: power factor 0."}]]}] 93:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Wattless current?"}]]}] 94:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"The component I sin φ at 90° to V; it does no work over a cycle."}]]}] 95:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Why use a choke rather than a resistor to limit AC?"}]]}] 96:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Its power factor is nearly zero, so it wastes almost no energy."}]]}] 97:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Resonant frequency of a series LCR circuit?"}]]}] af:Tb8f,

f_0 = 1/(2\pi\sqrt{LC})

98:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline","data-math":"inline","tabIndex":"$undefined","dangerouslySetInnerHTML":{"__html":"$af"}}],"."]}]]}] 99:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Impedance and current at resonance?"}]]}] 9a:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Z = R (least); I = V/R (greatest); power factor 1."}]]}] 9b:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Bandwidth of a series LCR circuit?"}]]}] b0:T4ba,

\Delta f = R/(2\pi L)

9c:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline","data-math":"inline","tabIndex":"$undefined","dangerouslySetInnerHTML":{"__html":"

\\Delta\\omega = R/L

"}}],", i.e. ",["$","span","code-1",{"className":"SmxAaG_mathInline","data-math":"inline","tabIndex":"$undefined","dangerouslySetInnerHTML":{"__html":"$b0"}}],"."]}]]}] 9d:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Q factor?"}]]}] b1:T148e,

Q = \omega_0L/R = \dfrac{1}{R}\sqrt{L/C} = \omega_0/\Delta\omega

9e:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline SmxAaG_mathInlineScroll","data-math":"inline","tabIndex":0,"dangerouslySetInnerHTML":{"__html":"$b1"}}],"."]}]]}] 9f:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"LC oscillations in one sentence?"}]]}] a0:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Energy passes back and forth between the electric field of C and the magnetic field of L."}]]}] a1:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Principle of the AC generator?"}]]}] a2:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Electromagnetic induction: a coil turned in a magnetic field has a changing flux."}]]}] a3:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Emf of a generator coil?"}]]}] b2:T4e3,

e = NBA\omega\sin\omega t

a4:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":[["$","span","code-0",{"className":"SmxAaG_mathInline SmxAaG_mathInlineScroll","data-math":"inline","tabIndex":0,"dangerouslySetInnerHTML":{"__html":"$b2"}}],"; peak ",["$","span","code-1",{"className":"SmxAaG_mathInline","data-math":"inline","tabIndex":"$undefined","dangerouslySetInnerHTML":{"__html":"

NBA\\omega

"}}]," when the plane is along B."]}]]}] a5:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Main advantage of AC over DC for the mains?"}]]}] a6:["$","div",null,{"className":"SmxAaG_md","lang":"$undefined","children":[["$","p","p-0",{"children":"Its voltage can be stepped up or down by transformers, so power is sent at high voltage with small loss."}]]}]

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