The law that connects the electric current flowing through a metallic resistor and the potential difference across its two ends is Ohm's law. According to Ohm's law, the current (I) flowing through a metallic resistor is directly proportional to the potential difference (V) across its two ends, given a constant temperature and other conditions. Mathematically, Ohm's law is expressed as:
V = I * R
where V is the potential difference across the resistor, I is the current flowing through the resistor, and R is the resistance of the resistor.
The condition under which Ohm's law is valid is when the temperature and other physical conditions remain constant. Ohm's law holds true for metallic resistors under normal operating conditions, where the material remains within its temperature limits and does not exhibit non-ohmic behavior.
For example, let's say we have a metallic resistor with a resistance of 10 ohms. If we apply a potential difference of 5 volts across the resistor, according to Ohm's law, the current flowing through the resistor would be:
I = V / R = 5V / 10Ω = 0.5 Amperes
Similarly, if we increase the potential difference to 10 volts, the current would become:
I = V / R = 10V / 10Ω = 1 Ampere
This demonstrates the direct relationship between the potential difference and current in accordance with Ohm's law.