When 120 V is applied to the filament of a 75 W lightbulb, the current drawn is

Question

When 120 V is applied to the filament of a 75 W lightbulb, the current drawn is 0.63 A. When a potential difference of 3 V is applied to the same filament, the current is 0.086 A. Is the filament made of an ohmic material? Explain your answer

(A) none of these

(B) No, the material is not ohmic. The resistance values for the two given voltages are the same.

(C) Yes, the material is ohmic. The resistance values for the two given voltages are the same.

(D) Yes, the material is ohmic. While the resistance of the material is different in each case, the temperature of the filament with 120 V across it is much greater than its temperature with only 3 V across it. Thus, the increased resistance is due to the temperature.

Explanation / Answer

let us assume that the material is ohmic
it means it will follow ohm's law that states that Voltage acorss an element=current through the element*resistance of the element

in first case, voltage=120 volts

current=0.63 A

resistance=120/0.63=190.48 ohms

when 3 volt is applied, current=0.086 A

then resistance=3/0.086=34.884 ohms

power when 120 volts applied=current^2*resistance=0.63^2*190.48=75.602 W

power when 3 V is applied=0.086^2*34.884=0.258 W

hence due to the large difference in heat dissipation values, temperautre of filament will be very different

hence depending upon the temperature coefficient of resistivity,

the material can have two different resistance values for two different voltage excitation

hence option D is correct.

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