What causes a voltage to appear across the secondary winding of a transformer when an AC voltage source is connected across its primary winding?
Why A transformer works because the changing current in the primary creates a changing magnetic flux in the core, and that flux links the secondary turns. By Faraday's law, a changing flux through a coil induces a voltage in it, and the shared-flux coupling between two coils is called mutual inductance. This is also why transformers only work on AC: a steady DC current makes no changing flux and no secondary voltage.
Watch out Capacitive coupling relies on an electric field between conductors separated by a dielectric, which is stray and unwanted in a transformer, not the mechanism that transfers power from primary to secondary.
Transformers are coils, and coils mean inductance: two coils sharing flux equals MUTUAL inductance.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the output voltage if an input signal is applied to the secondary winding of a 4:1 voltage step-down transformer instead of the primary winding?
Why A transformer's voltage ratio simply follows its turns ratio, Vp/Vs = Np/Ns, and it works in either direction. A 4:1 step-down transformer has four times as many turns on the primary as on the secondary, so feeding the signal into the low-turns secondary makes the high-turns winding the output and the voltage comes out four times larger. Running a step-down transformer backward turns it into a 1:4 step-up transformer.
Watch out Dividing by 4 is what happens in the normal direction, driving the high-turns primary and taking output from the low-turns secondary. The answers about adding resistance describe nothing the transformer ratio question asks about; turns ratio alone sets the voltage.
Feed a transformer backwards and the ratio flips: 4:1 down becomes 1:4 up, so voltage x4.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the total resistance of a 10-, a 20-, and a 50-ohm resistor connected in parallel?
Why For resistors in parallel you add the reciprocals: 1/R = 1/10 + 1/20 + 1/50 = 0.1 + 0.05 + 0.02 = 0.17 siemens. Inverting that gives R = 1/0.17 = 5.88 ohms, about 5.9 ohms. Note the sanity check: the parallel total is always smaller than the smallest single resistor, which here is 10 ohms.
Watch out The 0.17 ohm choice is the sum of the conductances before you take the reciprocal, and 80 ohms is what you would get by adding the three values as if they were in series.
Parallel total is always less than the smallest resistor. Don't forget the final 1/x keystroke.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the approximate total resistance of a 100- and a 200-ohm resistor in parallel?
Why Resistors in parallel combine as the product over the sum: (100 x 200) / (100 + 200) = 20000 / 300 = 66.7 ohms, which rounds to about 67 ohms. The total in a parallel network is always smaller than the smallest resistor present, because you are adding more paths for current. Here 67 ohms is indeed below the 100-ohm branch.
Watch out The 300-ohm choice is what you would get by adding them in series, and 150 ohms is just the average of the two values, which is not how parallel resistance works.
Parallel = product over sum, and the answer must be less than the smallest resistor.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Why is the primary winding wire of a voltage step-up transformer usually a larger size than that of the secondary winding?
Why An ideal transformer conserves power, so primary volts times primary amps equals secondary volts times secondary amps. In a step-up transformer the secondary voltage is higher, which means its current is proportionally lower, and the low-voltage primary must carry the larger current. Wire size is chosen by current-carrying capacity, so the high-current primary needs heavier gauge wire to keep I-squared-R heating and voltage drop down.
Watch out Coupling between windings is set by the core and winding geometry, not by wire gauge, so the choice about improving coupling is wrong; wire thickness only affects copper loss.
Step up the volts, step down the amps. Big current needs big wire, so the low-voltage side gets the fat wire.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the voltage output of a transformer with a 500-turn primary and a 1500-turn secondary when 120 VAC is applied to the primary?
Why Transformer voltage follows the turns ratio: Vsecondary = Vprimary x (Nsecondary / Nprimary). Here the ratio is 1500/500 = 3, so 120 V x 3 = 360 volts. More turns on the secondary than the primary means a step-up transformer, so the output voltage must be higher than the input.
Watch out The 40 volt choice is what you get by dividing 120 by 3, which would be correct only if the winding with 1500 turns were the primary (a step-down connection).
More turns out = more volts out. Multiply by secondary/primary: 120 x (1500/500) = 360.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What transformer turns ratio matches an antenna's 600-ohm feed point impedance to a 50-ohm coaxial cable?
Why Transformers change impedance as the square of the turns ratio: Z_primary/Z_secondary = (N_primary/N_secondary)^2. Here the impedance ratio is 600/50 = 12, so the turns ratio is the square root of 12, about 3.46, which rounds to 3.5 to 1.
Watch out The choice of 12 to 1 is the impedance ratio itself, not the turns ratio; squaring 12 would give a 7200 to 50 transformation.
Turns ratio = square root of impedance ratio. sqrt(600/50) = sqrt(12) = 3.5.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the equivalent capacitance of two 5.0-nanofarad capacitors and one 750-picofarad capacitor connected in parallel?
Why Capacitors in parallel add directly, just like resistors in series, because parallel plates effectively increase the total plate area. Convert to common units first: 750 pF = 0.75 nF, so 5.0 + 5.0 + 0.75 = 10.75 nF.
Watch out The 576.9 figure comes from working the series formula (and it would be picofarads, not nanofarads); series is the reciprocal rule, which always gives a value smaller than the smallest capacitor.
Capacitors: parallel adds. Two 5s plus 0.75 = 10.75 nF. Convert pF to nF before adding.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the capacitance of three 100-microfarad capacitors connected in series?
Why Capacitors in series combine like resistors in parallel: 1/C_total = 1/C1 + 1/C2 + 1/C3. For N identical capacitors that reduces to C/N, so 100 microfarads divided by 3 gives about 33.3 microfarads. Series always yields a total smaller than the smallest single capacitor, because you are effectively increasing the plate separation.
Watch out The choice of 300 microfarads is what you would get by adding them, which is how capacitors behave in parallel, not series.
Caps are backwards from resistors: series divides, parallel adds. Equal caps in series: just divide by how many.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the inductance of three 10-millihenry inductors connected in parallel?
Why Inductors in parallel combine like resistors in parallel: 1/Lt = 1/L1 + 1/L2 + 1/L3. With N identical inductors the total is simply L/N, so 10 mH divided by 3 gives about 3.3 mH. The result is always smaller than the smallest inductor in the group.
Watch out The 30 millihenry answer is what you would get by adding them, which applies to inductors in series, not parallel. The henry-valued choices are off by a factor of 1000 from the millihenry units given.
Inductors act like resistors: series adds, parallel divides. Equal parts in parallel = value/N, and answer stays in mH.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the inductance of a circuit with a 20-millihenry inductor connected in series with a 50-millihenry inductor?
Why Inductors in series add just like resistors in series: L_total = L1 + L2. So 20 mH + 50 mH = 70 mH. The magnetic fields of the coils (assuming no mutual coupling) simply add their opposition to changing current.
Watch out The 14.3 mH choice is the parallel result, from the product-over-sum formula (20 x 50)/(20 + 50), and 1,000 is just the product with no division.
Inductors behave like resistors: series adds, parallel divides. Capacitors are the opposite.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
What is the capacitance of a 20-microfarad capacitor connected in series with a 50-microfarad capacitor?
Why Capacitors in series combine like resistors in parallel: 1/Ct = 1/C1 + 1/C2, or for two capacitors the shortcut Ct = (C1 x C2)/(C1 + C2). Here that is (20 x 50)/(20 + 50) = 1000/70 = 14.3 microfarads. Note the result is smaller than either capacitor, which is always true for series capacitors because you are effectively increasing the plate spacing.
Watch out The 70 microfarad choice is just the sum, which is what you would get if the capacitors were in parallel; 1,000 microfarads is only the numerator of the product-over-sum formula, and 0.07 is the reciprocal of the answer.
Series caps: product over sum, and the answer must be SMALLER than the smallest capacitor.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Which of the following components should be added to a capacitor to increase the capacitance?
Why Capacitors in parallel add directly: C_total = C1 + C2 + ... Putting another capacitor across the first is electrically the same as enlarging the plate area, so the total charge stored per volt goes up. This is the opposite of resistors, which add in series.
Watch out Adding a capacitor in series lowers the total (1/C_total = 1/C1 + 1/C2), always giving less than the smallest capacitor. Inductors do not change capacitance at all; they form a resonant circuit with it.
Capacitors behave backwards from resistors: parallel adds, series divides. More plate area in parallel means more C.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.
Which of the following components should be added to an inductor to increase the inductance?
Why Inductors combine like resistors: in series the total is L1 + L2 + ..., so adding any inductor in series always gives a larger total inductance. In parallel they combine reciprocally (1/Lt = 1/L1 + 1/L2), which makes the total smaller than the smallest inductor. Capacitors do not add inductance at all; they store energy in an electric field and in combination with an inductor form a resonant circuit.
Watch out Putting another inductor in parallel is the tempting trap because more of something feels like more inductance, but parallel inductors divide down, just as parallel resistors lower resistance.
Inductors act like resistors: series adds up, parallel divides down. Capacitors are the mirror image.
HamSandwich explanation, first draft. The question and answers are the NCVEC text.