Question

The filament of a certain lamp has a resistance that increases linearly with temperature. When a constant voltage is switched on, the initial current decreases until the filament reaches its steady-state temperature. The temperature coefficient of resistivity of the filament is 4 times 10-3 K-1. The final current through the filament is one- eighth the initial current. What is the change in temperature of the filament 

          The filament of a certain lamp has a resistance that increases linearly with temperature. When a constant voltage is switched on, the initial current decreases until the filament reaches its steady-state temperature. The temperature coefficient of resistivity of the filament is 4 times 10-3 K-1. The final current through the filament is one- eighth the initial current. What is the change in temperature of the filament
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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The filament of a certain lamp has a resistance that increases linearly with temperature. When a constant voltage is switched on, the initial current decreases until the filament reaches its steady-state temperature. The temperature coefficient of resistivity of the filament is 4 times 10-3 K-1. The final current through the filament is one- eighth the initial current. What is the change in temperature of the filament
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The filament of an incandescent light bulb is made of tungsten, which has a thermal coefficient of resistivity of a = 4.4x10^-3 K^-1. The filament is initially at room temperature, T0 = 293 K. When it is connected across a V = 130 volt power supply, the filament quickly heats up to T = 2700 K, at which time the current flowing through the filament is I = 0.75 amps. Write an equation for the initial current, I0, that flows through the filament when it is initially turned on (when it is still at room temperature). I0 = ?

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The filament of an incandescent light bulb is made of tungsten, which has a thermal coefficient of resistivity of a = 4.4x10^-3 K^-1. The filament is initially at room temperature, T0 = 293 K. When it is connected across a V = 130 volt power supply, the filament quickly heats up to T = 2700 K, at which time the current flowing through the filament is I = 0.75 amps. Write an equation for the initial current, I0, that flows through the filament when it is initially turned on (when it is still at room temperature). I0 = ?

Sri K.
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Transcript

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00:01 In this question here, we have told that the temperature coefficient is alpha equals to 4 multiplied by 10 power minus 3 k inverse.
00:24 Now the resistance of the filament is mathematically represented as r equals to r node multiply by 1 plus alpha.
00:38 Delta t where r nod is the initial resistance initial resistance so here making the change in temperatures to subject of the of that formula so here we can write rewrite as delta t equals to 1 divided by alpha multiply by r divided by r nod minus 1 now from om law, from om's law, we know that i equals to v divided by r.
01:35 So this imply that current varies inversely with current.
01:42 So here we can write as r divided by r0 is equals to i not divided by i not divided by i...
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