Induced current; Different voltage ??

Hey,
One of my friend asked me the following question and I couldn't answer it. In the diagram below B is varying with time thus induces current I. What is Vs? Is it I*1k[v] or I*1[v]? Any help?

Here is the diagram

hmm i belive it depends on which I are u talking about... their both right in a way... different currents flow through each resistor but Ik*1k=Io*1, where Ik is the current that flows through 1k resistor and Io is the current that flows through 1ohm resistor.

ho can you have different current when the resistors are connected in a loop. According to KCL current must be same.

oh now i see what u mean... i saw those leads coming out of the loop and thought of something else... but u can not apply KCL in a loop as far as i know. kirchoff in a loop deals with voltage not currents. And to answer ur question i doubt there will be any current induced if u have that loop in a varying magnetic field but i cant say for sure.

The voltage, as you have drawn it, would be I*1ohm. The tricky part here is that the voltages across each resistor are NOT equal!

KVL states that the sum of the voltages around the loop equals zero; however, KVL is formulated from maxwell's equations for the special case that there is no changing magnetic flux. If there is, then the sum of the voltages around the loop is NOT zero, and instead depends on the changing flux.

Therefore, since there is a changing flux, the voltage directly across the 1k ohm resistor is not the same as the voltage across the 1 ohm resistor. You can still find the current in the loop from knowledge of the magnetic field, and use that with ohm's law to find the voltage on either resistor.

thanks that sure makes sense for me