# A long, fine wire is wound into a coil with inductance 5 mH. . .

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A long, fine wire is wound into a coil with inductance 5 mH. The coil is connected across the terminals of a battery, and the current is measured a few seconds after the connection is made. The wire is unwound and wound again into a different coil with L = 10 mH. This second coil is connected across the same battery, and the current is measured in the same way. Compared with the current in the first coil, is the current in the second coil

A. unchanged

B. half as large

C. one-fourth as large

D. twice as large

E. four times as large

Relevant equation: L = N(phiB)/I

Solving for I, I = N(phiB)/L. So why is it that when L changes from 5 mH to 10mH that the current isn't half as large? Assuming N(phiB) doesn't change from one coil to the next, the ratio of I2(current in second coil) to I1(current in first coil) is 1/2.

Am I allowed to assume N(phiB) doesn't change from one coil to the next? Or would N also double since N and L are directly related in the original equation, which would make the current unchanged?