A primary coil is connected to a DC
voltage source and placed inside a secondary coil. When the circuit of the primary
coil is opened, which of the following options best describes the current in the
secondary coil? a) Forward induced current, b) backward induced current, c)
alternating current, d) direct current.
To start out, let’s make a sketch
of this primary coil. In this circuit loop, we know we
have a DC power supply and a coil of wire. And we’ve drawn in a switch that we
can close or open at will. We know that if we close the
switch, the circuit will be complete and current will begin to flow through this
This current-carrying loop though
isn’t the only part of our setup. We also have a secondary coil which
surrounds the primary coil. That secondary coil could look like
this. And if we saw the coils end on, we
would see the primary coil inside the loops of the secondary coil.
When the switch to our initial
current loop is closed, we know that steady current will flow through this
circuit. And we can say that the
steady-state current amount is capital 𝐼. And we can say that the direction
of 𝐼, the direction of current in this loop, is to be considered the forward
direction. This is the steady-state condition
of our circuit.
But we’re told that a change is
made, that the primary coil is opened up. When this happens, when our switch
opens and the current suddenly stops flowing, a drastic change occurs. For one thing, the current in the
circuit changes very rapidly. If we call that change in current
Δ𝐼 divided by Δ𝑡, we know the direction of the change would be opposite the
direction of the original current flow.
We could say then that a changing
current is running counterclockwise now through our primary coil loop. That changing current has an effect
on the magnetic field in the loops of the primary coil. Thanks to the change in current, a
change in the magnetic field is created. We can call it Δ𝐵 sub 𝑝 to say
that it’s the change in the magnetic field created by the primary coil.
If our secondary coil wasn’t
present, this might be the end of the effect. But because of the secondary coil,
more phenomena occur. And that’s because this changing
magnetic field, Δ𝐵 sub 𝑝, is experienced through the loops of the secondary
coil. And it’s opposed by that coil
thanks to Lenz’s law. That means an opposing magnetic
field will be induced in the secondary coil loops. We’ll name it 𝐵 sub 𝑠 to specify
that it’s created by the secondary coil.
This new magnetic field, 𝐵 sub 𝑠,
will induce an emf in the secondary coil which will drive current. And the question is, which way
through the loop will the current go? If we use our right-hand screw
rule, we can tell that the induced current in the secondary coil will flow in this
direction, clockwise from our perspective.
Notice that this current, which we
can call 𝐼 sub 𝑠, is flowing in the direction we defined as forward in our primary
coil loop. Furthermore, this current is an
induced current. And therefore, as we look over our
four answer choices, we see that the choice that matches best is choice a). When the steady-state current flow
in the primary coil is interrupted, then the current in the secondary coil will be
forward induced current.