Question Video: Identifying the Different Currents in an Alternating Current Circuit | Nagwa Question Video: Identifying the Different Currents in an Alternating Current Circuit | Nagwa

# Question Video: Identifying the Different Currents in an Alternating Current Circuit Physics • Third Year of Secondary School

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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.

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### 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. Letโs 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 ๐ผ๐. 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, letโs 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.

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