Two circular loops lie side by side in the same plane. One is connected to a source that supplies an increasing current; the other is a simply closed ring. Is the induced current in the ring in the same direction as the current in the loop connected to the source, or the opposite? What if the current in the first loop is decreasing? Explain.

The direction of any magnetic induction effect is such as to oppose the cause of the effect.

The direction of the magnetic field due to current carrying loop

If the current is flowing in anti-clockwise direction then the direction of the magnetic field will be out of the plane.

If the current is flowing in a clockwise direction then the direction of the magnetic field will be inward of the plane.

As the first circular loop is getting an increasing current, then it produces the magnetic field depending on the direction of the supply current which passes through the second loop that changes the magnetic flux of the second loop.

Now, there is a change in magnetic flux through the second loop which causes an induced current in opposite direction to the supply current in the first loop (Lens law).

If the current in the first loop is decreasing then it results in decreasing magnetic flux through the second loop.

Hence according to lens law, the current should flow in such a direction that increases the input magnetic flux. Then the current in the second loop flows in the opposite direction.