### Video Transcript

The graph contains a black line
representing the changes to the voltage with time in a circuit connected to an
alternating current source. The three colored lines represent
the changes of the current with time in the circuit depending on the properties of
the circuit. Which of the following combinations
correctly shows the correspondence between the colors of the lines and the
properties of the circuits with the currents represented by these lines? (A) Red line for a capacitive
circuit, orange line for an inductive circuit. (B) Orange line for a capacitive
circuit, red line for an inductive circuit. (C) Orange line for a capacitive
circuit, blue line for an inductive circuit. (D) Blue line for a capacitive
circuit, orange line for an inductive circuit. (E) All these combinations are
possible.

In this question, we are being
asked to identify each colored line with the corresponding type of circuit in an
alternating-current circuit. Letโs recall the different types of
circuits and their graphs.

A resistive circuit is a circuit
containing a resistor. The current in such a circuit is
completely in phase with the emf, since they are proportional to each other, as we
can see from the equation ๐ is equal to ๐ผ๐
. We also know that an
alternating-current circuit can contain a capacitor, represented by two nearby lines
in circuit diagrams. Such a circuit is called a
capacitive circuit.

In AC capacitive circuits, the
potential difference through the capacitor and the charge accumulation current are
not in sync with each other. The change in current leads to the
change in potential difference by 90 degrees or ๐ by two radians. Finally, an AC circuit can also
contain an inductor, represented by a curved line in the circuit diagrams. In AC inductive circuits, the
change in current is 90 degrees, or ๐ by two radians, behind the change in
potential difference.

Looking now back at the original
diagram, letโs identify each colored line with its appropriate type of circuit.

The line that corresponds to the
circuit that is only resistive should be the line that matches the curves of the
emf, as they are directly in phase with each other. This can be only the blue line. Now then, we expect the line
representing the capacitive circuit to be 90 degrees, or ๐ by two radians, ahead of
the emf. Comparing this with the lines we
have been given, we can see that this description most closely matches the orange
line, as its peaks are before the emf. Finally, the emf will lead the line
representing the inductive circuits current by 90 degrees, or ๐ by two. This means that the peak of the
line of the inductive current will be after the emf peaks, which appears to fit
quite well with the red line.

Taking all of this into
consideration, we can deduce that the answer that we are looking for must be option
(B): the orange line for a capacitive circuit, red line for an inductive
circuit.