Voltage across coiled wire with varying electric current

[sparkle123]

A varying electric current running through a coiled wire induces an emf across the coil. The voltage measured by a voltmeter across the terminals of the coil:
(a) is smaller or larger than the emf, depending on how fast the current changes.
(b) is larger than the emf.
(c) is equal to the emf.
(d) is smaller than the emf.

The answer is (d) but I thought it was (b).
My reasoning is that a voltage V is required to get the current running in the positive direction. Say the current is increasing in the positive direction. Then the magnetic flux is also increasing, so an induced emf in the negative direction is produced.
The measure voltage M = V - emf and since emf is relatively small, M > emf.

Thank you! :)

 

[jbsteele]

No, your reasoning is incorrect. The induced emf opposes the applied voltage, so the measured voltage (M) will be less than the applied voltage (V). Therefore, the answer is (d), the measured voltage is smaller than the emf.