A primary coil of wire is connected to a DC voltage source and placed within a secondary coil. When the primary coil is opened, current in the secondary coil will be a) forward-induced current, b) backward-induced current, c) alternating current, d) direct current.
We can start on our solution by sketching out this scenario. Here we have a primary coil of wire connected to a DC source. And we’re told this primary coil is enclosed within a larger secondary coil. We’re told then that the primary coil is opened, say, by a switch opening up, which breaks the loop. And based on that change, we want to know about the current in the secondary coil.
To figure this out, let’s consider what was happening in our system before the primary circuit was opened. With this switch closed, steady current — we can call it 𝐼 — was running through our primary coil supplied by this DC source. Because the current was constant, therefore, the magnetic field created within the loops of the primary coil was also steady. This means that there was no induced EMF in the secondary coil, so long as the current, 𝐼, is a constant current.
When it comes to current direction, we can define the direction of 𝐼 as forward in this circuit. When the primary coil is opened up, that means current suddenly stops flowing in this coil. The rate of change of current therefore is backward through the circuit.
We could say that when the circuit is broken, there’s effectively an increase in current moving backward through the primary coil and that this increase produces a magnetic field which increases in the windings of this coil. We’ll call this increasing magnetic field 𝐵 sub 𝑝 to identify that it’s caused by the primary coil.
We know that, in response to this changing magnetic flux through its coil, current will be induced in the secondary coil. Moreover, that current will be induced to oppose the change of flux. In other words, current will be induced in the secondary coil in such a direction that it creates a magnetic field which opposes 𝐵 sub 𝑝. We’ll call this 𝐵 sub 𝑠, the field induced by the secondary coil.
Using the right-hand rule, if we were to sketch in the direction of the current induced in the secondary coil, we see it would move clockwise, the same as the direction as the original current in the primary coil. Since we defined that original direction as forward, that means that the induced current in the secondary coil is also forward. This means we choose answer choice a forward-induced current.