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Two wires of the same material are both connected to a 9-V ideal battery. They have the same cross section area but wire 2 is twice longer than wire 1. Compare the following quantities by answering if the quantity for wire 1 is smaller, equal or greater than the same quantity in wire 2.

  • Current in wire 1 vs. current in wire 2.

  • Electric field in wire 1 vs. electric field in wire 2.

The solutions say that current 1 = current 2 and that electric field 1 = electric field 2.

How does the length of the wire affect these two quantities? According to Kirchhoff's Law: $\Delta V=RI$.

$R=\frac{L\rho}{A}\implies$ Resistance of wire 2 is twice the resistance of wire 1. Therefore, the current in wire 2 will be twice as small as wire 1.

Finally, we know that $J=\sigma E$ The resistivity is the same because the material is the same. So, the electric field will be twice as small for wire 2.

The solutions manual seems wrong. Am I right or is there a problem in my reasoning?

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    $\begingroup$ The question is ambiguous; it isn't specified if the wires are parallel connected or series connected. If parallel connected, the voltage across each wire is identical. If series connected, the current through each wire is identical. The solution given is for series connected wires. $\endgroup$
    – Alfred Centauri
    Commented Apr 12, 2015 at 1:28

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In this case,if they are connected one at a time to the battery then, your reasoning is correct. But if both are connected at same time in series, then current will be same and electric field will also be same.

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