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E5B

ELECTRICAL PRINCIPLES

Time constants and phase relationships: RL and RC time constants; phase angle in reactive circuits and components; admittance and susceptance

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E5B011 of 12

What is the term for the time required for the capacitor in an RC circuit to be charged to 63.2% of the applied voltage or to discharge to 36.8% of its initial voltage?

Why In an RC circuit the voltage across the capacitor changes exponentially, and the characteristic time of that exponential is the time constant, tau = R times C (in an RL circuit tau = L/R). After one tau the capacitor has charged to 1 - 1/e = 63.2% of the applied voltage, or discharged to 1/e = 36.8% of its starting voltage. After about five time constants the circuit is considered fully charged or discharged.
Watch out The other choices are invented phrases; there is no standard quantity called an exponential period or a time factor in RC analysis.
63.2% up, 36.8% down = one time constant. Tau = R x C, and 5 tau means done.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B022 of 12

What letter is commonly used to represent susceptance?

Why Admittance is the reciprocal of impedance, and just as impedance is written Z = R + jX, admittance is written Y = G + jB. In that pairing the real part G is conductance (the reciprocal counterpart of resistance) and the imaginary part, susceptance, is the reciprocal counterpart of reactance and carries the letter B. Susceptance is measured in siemens, the same unit as conductance and admittance.
Watch out Y is tempting because it is the admittance itself, the complete complex quantity, not just its reactive part; G is conductance and X is reactance in the impedance form.
Z = R + jX flips to Y = G + jB. Susceptance is the B in that pair.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B033 of 12

How is impedance in polar form converted to an equivalent admittance?

Why Admittance is simply the reciprocal of impedance, Y = 1/Z. In polar form, dividing 1 by M at angle theta gives (1/M) at angle minus theta, because reciprocals invert the magnitude and negate the phase angle. So a 50 ohm impedance at +30 degrees becomes an admittance of 0.02 siemens at -30 degrees.
Watch out The choice that inverts the angle and flips the sign of the magnitude has the two operations backwards; magnitudes of impedance and admittance are always positive, and it is the phase that changes sign.
Y = 1/Z: flip the magnitude, flip the sign of the angle.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B044 of 12

What is the time constant of a circuit having two 220-microfarad capacitors and two 1-megohm resistors, all in parallel?

Why Time constant for an RC circuit is tau = R times C. Capacitors in parallel add, so two 220 uF caps give 440 uF. Resistors in parallel halve, so two 1 megohm resistors give 0.5 megohm. tau = 440e-6 F x 0.5e6 ohms = 220 seconds.
Watch out The choice of 440 seconds comes from adding the capacitors but forgetting that parallel resistors halve; 110 seconds comes from halving both values as if the capacitors were in series too.
Parallel: caps add, resistors divide. 440 uF x 0.5 M = 220 s.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B055 of 12

What is the effect on the magnitude of pure reactance when it is converted to susceptance?

Why Susceptance is the reciprocal of reactance, just as conductance is the reciprocal of resistance. For a pure reactance, B = -1/X, so a 50 ohm reactance becomes 0.02 siemens of susceptance. The question asks about magnitude, and taking the reciprocal is what changes the number's size.
Watch out The choice about reversing the sign describes what happens to the sign in B = -1/X (an inductive reactance gives negative susceptance), but that is not a change in magnitude.
Susceptance is reactance flipped over: B = -1/X. Magnitude reciprocal, sign flipped.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B066 of 12

What is susceptance?

Why Admittance Y is the reciprocal of impedance, Y = 1/Z, and like impedance it has two parts: Y = G + jB, where G is conductance (the real part) and B is susceptance (the imaginary part). Susceptance is the reciprocal-style measure of reactance in a parallel circuit, expressed in siemens, and it is positive for capacitance and negative for inductance in this convention. Using admittance makes parallel circuits easy because conductances and susceptances simply add.
Watch out The choice about magnetic impedance is a made-up term, and the ratio of electric to magnetic field is the wave impedance of a medium, not susceptance.
Impedance = R + jX; flip it over and you get Admittance = G + jB. B is the imaginary half, susceptance.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B077 of 12

What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 500 ohms, R is 1 kilohm, and XL is 250 ohms?

Why In a series RLC circuit the reactances subtract: X = XL - XC = 250 - 500 = -250 ohms, so the net reactance is capacitive. The phase angle is arctan(X/R) = arctan(250/1000) = 14.0 degrees. Because the circuit is net capacitive, the current leads the voltage, which is the same as saying the voltage lags the current.
Watch out The 14.0 degrees with voltage leading choice has the right magnitude but the wrong sign; voltage leads only when XL is larger than XC (net inductive). The 68.2 degree answers come from flipping the ratio and taking arctan(1000/250).
ELI the ICE man: with C dominant (ICE), current leads. Angle = arctan(net X / R), here arctan(250/1000) = 14 degrees.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B088 of 12

What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 300 ohms, R is 100 ohms, and XL is 100 ohms?

Why In a series RLC circuit the reactances subtract: X = XL - XC = 100 - 300 = -200 ohms, so the net reactance is capacitive. The phase angle is arctan(X/R) = arctan(-200/100) = arctan(-2) = -63 degrees. A capacitive circuit makes current lead the voltage, which is the same thing as saying the voltage lags the current.
Watch out The choice with voltage leading by 63 degrees has the right magnitude but the wrong sense; that would be an inductive circuit where XL exceeds XC. The 27 degree answers come from taking arctan(R/X) instead of arctan(X/R).
ELI the ICE man: in ICE (capacitive), I comes before E, so current leads and voltage lags. tan(angle) = (XL-XC)/R.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B099 of 12

What is the relationship between the AC current through a capacitor and the voltage across a capacitor?

Why A capacitor's current depends on the rate of change of voltage: i = C(dv/dt). Current is therefore largest when the voltage is changing fastest (as it crosses zero) and zero when the voltage is at its peak, which puts the current one quarter cycle, or 90 degrees, ahead of the voltage. This is the opposite of an inductor, where the voltage leads the current by 90 degrees.
Watch out The choice saying voltage leads current by 90 degrees describes an inductor, not a capacitor; in phase would describe a pure resistance.
ELI the ICE man: in a Capacitor (C), I comes before E, so current leads voltage.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B1010 of 12

What is the relationship between the AC current through an inductor and the voltage across an inductor?

Why In an inductor the voltage is proportional to the rate of change of current, V = L(di/dt). The current must start changing before any voltage appears in response, so the voltage waveform reaches its peak a quarter cycle ahead of the current peak. That quarter cycle is 90 degrees, so voltage leads current by 90 degrees in a pure inductance.
Watch out The choice saying current leads voltage by 90 degrees describes a capacitor, where the current must flow first to build up the charge that creates the voltage.
ELI the ICE man: in L, E (voltage) leads I; in C, I leads E.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B1111 of 12

What is the phase angle between the voltage across and the current through a series RLC circuit if XC is 25 ohms, R is 100 ohms, and XL is 75 ohms?

Why In a series RLC circuit the reactances subtract: X = XL - XC = 75 - 25 = 50 ohms, and the net result is inductive since XL is larger. The phase angle is arctan(X/R) = arctan(50/100) = arctan(0.5), about 27 degrees. Because the net reactance is inductive, the voltage leads the current (ELI: E leads I in an inductor).
Watch out The 63 degree choices come from flipping the ratio and taking arctan(R/X) = arctan(100/50); the tangent of the phase angle is always reactance over resistance. The lagging choices would apply only if the net reactance were capacitive, meaning XC larger than XL.
ELI the ICE man: net XL wins, voltage leads. Angle = arctan(X/R), reactance on top.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
E5B1212 of 12

What is admittance?

Why Admittance, symbol Y, is defined as the reciprocal of impedance: Y = 1/Z, measured in siemens (formerly mhos). Just as impedance is the complex sum of resistance and reactance, admittance is the complex sum of conductance G and susceptance B. Working in admittance makes parallel circuits easy, because admittances simply add in parallel the way impedances add in series.
Watch out The inverse of reactance alone is susceptance, not admittance; admittance is the inverse of the whole complex impedance. The field effect transistor choices belong to a different topic entirely (transconductance and on-resistance).
Flip the whole thing: 1/Z = Y (admittance); flip just the reactive part: 1/X = B (susceptance).
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
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