I choose an inductor of 1uH with a series resistance calculated to drop the required voltage (taking the capacitor into account).

Resonance is the State where X(C)==X(L)

No, try Xc = -Xl.

 

120V mains is relatively benign compared to the voltage in the resonant circuit!

But it's NOT resonant....that's the whole point. There are two possible solutions, one on the high side of resonance, and one on the low side. The important factor is the net reactance...and for this problem, the sign of the net reactance doesn't matter.

 

But it's NOT resonant....that's the whole point. There are two possible solutions, one on the high side of resonance, and one on the low side. The important factor is the net reactance...and for this problem, the sign of the net reactance doesn't matter.

"Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts." Wikipedia

 

View attachment 301458
You have a 12volt 25 watt lamp that you need to run off of house current (120VAC, 60 Hz in the U.S.). You can drop the voltage to the proper voltage efficiently using just series reactance. With the circuit above, what value of L1 do you need to make the lamp happy? (Capacitor C1 is non-negotiable.)

What I like about this sort of problem is that there are several very different approaches to figuring it out. It's a great exercise in sanity checks. One way I like is to FIRST figure out the power factor. (P.S., I used ICAP4 to draw this, which doesn't have a lamp model, so I had to roll my own. ) We know that the total circuit current is the same as the lamp current, which is 25/12 or 2.08 amps. So the circuit apparent power is 120x2.08 or 249.6 W (we can round up to 250W. The True power is 25 watts, because the lamp is the only thing that dissipates power. So the power factor is 25/250 or 0.1.
Now, once we know the power factor, we can figure out the phase angle., the arccosine of .1. or 84.26 degrees.

continued....

 

What I like about this sort of problem is that there are several very different approaches to figuring it out. It's a great exercise in sanity checks. One way I like is to FIRST figure out the power factor. (P.S., I used ICAP4 to draw this, which doesn't have a lamp model, so I had to roll my own. ) We know that the total circuit current is the same as the lamp current, which is 25/12 or 2.08 amps. So the circuit apparent power is 120x2.08 or 249.6 W (we can round up to 250W. The True power is 25 watts, because the lamp is the only thing that dissipates power. So the power factor is 25/250 or 0.1.
Now, once we know the power factor, we can figure out the phase angle., the arccosine of .1. or 84.26 degrees.

continued....

Now the next morsel of information we need is the circuit RESISTANCE, which is simply the lamp resistance, which is 25V/2.08 or 5.77 ohms. Oh yes, we also know the total circuit Z, which is 120/208 which is 57.7 ohms. Now all we need to do is calculate the required reactance. Z^2 = R^2 + X^2. Now solve for X

 

If the phase angle is 84° then the real part of the impedance is negligible and an assumption that the circuit is entirely reactive will give less error than the component tolerances. (I've been in the real world too long to believe in absolute component values)

 

If the phase angle is 84° then the real part of the impedance is negligible and an assumption that the circuit is entirely reactive will give less error than the component tolerances. (I've been in the real world too long to believe in absolute component values)

It is certainly MOSTLY reactive, but this circuit actually works.
In my electronics classes, someone invariably asks, "What should we use for pi...3.14159 or 3.1416?" I always tell them, "How about 3.1?" I then explain that since resistor color codes only have two significant digits, it's pointless to use more than two significant digits for PI in any calculation. Of course, for instrumentation we want higher precision, but just about ANY radio circuit will basically function with 20% tolerances.

 

but this circuit actually works.

Provided that you didn't assume that a 120V AC rated capacitor would be adequate!

 

We weren't taught that in our school .

The squaw on the hippopotamus is equal to the sum of the squaws on the other two hides.

 

 

View attachment 301502

I do like unity-power-factor beer - dispensed by gravity from a cask behind the bar, served at room temperature.

 

In practice such a circuit will show a poor performance.
When we were students, we made a night light in the living room, an incandescent lamp (3.5V 0.25A) was connected in series with a capacitor and powered from the mains . It was lit dimly , 24/7. Lifespan was about one week only. Guess why this happened?

 

We weren't taught that in our school .

You say me an impossible thing.... Its actually the 5th or 6th grade thing in geometry.
Here in our case the capacitive current is (b) upward, the (b) downward is inductive current, the (a) is active current and (c) is complex current absolute value.
https://en.wikipedia.org/wiki/Pythagoras

 

In practice such a circuit will show a poor performance.
When we were students, we made a night light in the living room, an incandescent lamp (3.5V 0.25A) was connected in series with a capacitor and powered from the mains . It was lit dimly , 24/7. Lifespan was about one week only. Guess why this happened?

You used and electrolytic capacitor. I would recommend an oil motor-start capacitor.

 

You say me an impossible thing.... Its actually the 5th or 6th grade thing in geometry.
Here in our case the capacitive current is (b) upward, the (b) downward is inductive current, the (a) is active current and (c) is complex current absolute value.
View attachment 301557https://en.wikipedia.org/wiki/Pythagoras

Are you in the U.S.? Here at least, by convention Inductive reactance is up, capacitive down. But again, that might just be US.

 

You used and electrolytic capacitor. I would recommend an oil motor-start capacitor.

Oh, man , no, no. I did knew what for is an electrolytic capacitor... It was a paper-in-oil capacitor, rated to 250VAC.
Lamp's lifespan was a week or so. A week only