# Confusion about the relationship between current, resistance and potential difference

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?

• More of a context is required to answer your question. Is the book referring to ohmic or non-ohmic conductors? – Farcher Oct 22 '19 at 7:08
• 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. – borns Oct 22 '19 at 7:12
• But the key says temp decreases and thus resistance decreases( the arrangement is in series) – borns Oct 22 '19 at 7:30
• A light bulb filament is a temperature dependent resistor. When the temperature drops, the resistance drops. – Bill Watts Oct 22 '19 at 7:46

## 1 Answer

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.