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A 110 V lamp 16 C.P. and a lamp of the same material and worked at the same efficiency develops 25 CP on 220 V. The ratio of diameters of the filaments will be

The power of a lamp is directly proportional to the fourth power of its diameter.

So, let the ratio of diameters of the filaments be x, then we have:

(Power of 110 V lamp)/(Power of 220 V lamp) = (Voltage of 110 V lamp/Voltage of 220 V lamp)? * (Diameter of 110 V lamp/Diameter of 220 V lamp)?

(16/x²)/(25/1) = (110/220)? * (1/x)?

Simplifying the above equation, we get:

16/25 = 1/16 * 1/x?

x? = 16/25 * 16 = 10.24

Taking the fourth root of both sides, we get:

x = 1.78