If the voltage of a component has dropped, what will happen to the resistance? My book says it will decrease but I don't understand the logic. How can current and resistance go down at the same time? Please explain in easy words. Question The dc power supply is set to 12 V and the ammeter reading is 1.5 A. The student changes the emf of the dc power supply to 6 V. The lamp dims and the ammeter reading changes. What happens to the resistance of the filament lamp?
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$\begingroup$ More of a context is required to answer your question. Is the book referring to ohmic or non-ohmic conductors? $\endgroup$– FarcherCommented Oct 22, 2019 at 7:08
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$\begingroup$ All that's told is a variable dc power supply is being used and its voltage has been dropped from 12 V to 6 V, which has caused a decrease in current. $\endgroup$– bornsCommented Oct 22, 2019 at 7:12
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$\begingroup$ But the key says temp decreases and thus resistance decreases( the arrangement is in series) $\endgroup$– bornsCommented Oct 22, 2019 at 7:30
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$\begingroup$ A light bulb filament is a temperature dependent resistor. When the temperature drops, the resistance drops. $\endgroup$– Bill WattsCommented Oct 22, 2019 at 7:46
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1 Answer
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The answer key is correct! The conductivity and resistivity of any metal is dependant on temperature. The resistivity at Celsius temperature $t$ is given by:
$$\rho=\rho_{20}[1+\alpha(t-20^\circ C)] \space ,$$
See the resistivities and temperature coefficients below:
Moreover, we have:
$$R=\frac{L}{A}\rho \space ,$$
where $L$ is the length of the wire, and $A$ is its cross-sectional area. When the voltage is dropped, the current reduces, then the LED filament becomes cooler and its resistance $R$ decreases.
answered Oct 22, 2019 at 8:37