Which of the two bulbs has more filament resistance: 15 watt or 70 watt operating at the same voltage?

The power of the electric current is determined by the following expression:
P = U * I
Ohm’s law for a chain section:
I = U / R
Let’s plug this into the expression for the cardinality:
P = U * I = U² / R
Let us express from this expression resistance:
R = U² / P
By condition, our voltage is the same, resistances are determined by the following expressions:
R1 = U² / P1
R2 = U² / P2
Let’s divide R1 / R2:
R1 / R2 = (U² / P1) / (U² / P2) = P2 / P1
Substituting the numerical values, we get:
R1 / R2 = P2 / P1 = 70/15 = 4.66
Answer: the resistance of the first light bulb (15 W) is 4.6 times greater.



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