Question

The potential difference across the ends of a wire is doubled in magnitude. If Ohm's law is obeyed, which one of the following statements concerning the resistance of the wire is true?a- The resistance is one half of its original value.b- The resistance decreases by a factor of four.c- The resistance is twice its original value.d- The resistance is not changed.e- The resistance increases by a factor of four.

Answer 1

Given:

The potential difference across the ends of a wire is doubled in magnitude

To find:

which one of the following statements concerning the resistance of the wire is true

Step-by-step explanation:

The potential difference is doubled in magnitude. We know, according to Ohm's law,

`V=IR`

I is the current and R is the resistance.

If the potential difference increases, the product of I and R also increases.

Now the resistance depends as,

`\begin{gathered} R=(\rho l)/(A) \\ \rho\text{ is the resistivity, l is the length and A is the area of the conductor.} \end{gathered}`

The resistance is independent of potential differences. When the potential difference increases, the current also increases and the resistance remains the same.

Hence, The resistance is not changed.