[morzh]

Rod,

You are right, but then I am right also.

The pilot lamp is a separate load, in parallel to the filaments; so I do not need to protect the lamp, as I don't care about it, plus it is todays lamp for 130V, and I bought 10pcs from Amazon at $1.50 ea. This is a lifetime supply.



Vlad,

You would be right. But, as said before, I calculated a capacitor. Not a resistor.
Hint: there is a phase shift of 90 degrees.

So the formula that applies is not that for series ohmic resistances (or reactances of the same type) which is

R1 + R2 = R3,

but for reactances (in this case a capacitive one, let's call it Zc) in series with Ohmic resistance ®, which is: (we will call the total impedance Z)

R-square + Zc-square = Z-square (Formula #1)

This is, as you might remember, what we learnt in...9th year of school and, of course, in the course of circuit theory.

So. Here's the calcs:

The sum of the filaments' voltages (nominal) is 115V.
We will call existing resistance "R-115" and the impedance needed to obtain the same current at 127V "Z-127".
The capacitive reactance is Zc.
The capacitance is C.

The resistance of the existing filament string is
R-115 = 115V/0.15A = 767 Ohm.

The impedance needed for 127V is
Z-127 = 127/0.15A = 846.7 Ohm.

Now we solve for Formula #1:

R-square + Zc-square = Z-square
767-square + Zc-square = 846-square.
Or
588289 + Zc-square = 716844

Now

Zc-square = 716844-588289 = 128555

And the Zc is
Zc = SQRT(128555)
Zc = 359 Ohm.

So. Your capacitive reactance that would increase the impedance by some 77 Ohm is not, well, 77 Ohm but 359 Ohm.
Phase shift. Have to deal with it.

The communist party teaches us the water bopils at 90 degrees C!!!

Now, calculating the cap is easy, it is (F = 60Hz, C is capacitance in Farads)
Zc = 1/(6.28*F*C).
So,
C = 1/(Zc * 6.28 * F) = 1/ (359 * 6.28 * 60) = 1 / 135271 = 0.0000074 F = 7.4 uF.


Done.