Why does the voltage across a wire with current in it equal zero?

[Caboose23]

My teacher gave us claims for homework and we have to prove them. I am having trouble with these two:

• the voltage across the ends of a wire with current in it is zero
• it doesn't matter across which device (light bulb, resistor, etc.) you measure the voltage in a parallel circuit

 

[StatusX]

For the first one, that is sort of a definition. In reality, there is a voltage drop across every part of the circuit, but across a wire it is very small. We usually pretend the wires are ideal, and that the drop is exactly zero.

For the second one, use kirchhoffs voltage loop law, that the total voltage drop around any closed loop in a circuit must be zero.

 

[thepatientmental]

The voltage across a wire with current in it equals zero because of Ohm's Law, which states that the voltage (V) is equal to the current (I) multiplied by the resistance (R). In a wire, the resistance is very low, so even with a current flowing through it, the voltage drop across the wire is negligible. This means that the voltage at both ends of the wire will be essentially the same, resulting in a voltage difference of zero.

In a parallel circuit, the voltage is the same across all devices connected in parallel. This is because in a parallel circuit, each device has its own separate path for current to flow through. So, in a parallel circuit, the voltage drop across each device will be the same, regardless of which device you measure it across. This is why the voltage across a wire with current in it will be zero, even if you measure it across a different device in the parallel circuit.

In conclusion, the voltage across a wire with current in it is zero due to the low resistance of the wire and the fact that the voltage in a parallel circuit is the same across all devices. This is a fundamental principle in electrical circuits and is supported by Ohm's Law.