Question Video: Graphically Representing Properties of Alternating Current Circuits Physics • 9th Grade

The graph contains a black line representing the changes of 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 color line corresponds to the circuit being only resistive? Which color line corresponds to the circuit being capacitive? Which color line corresponds to the circuit being inductive?

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Video Transcript

The graph contains a black line representing the changes of 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 color line corresponds to the circuit being only resistive? Which color line corresponds to the circuit being capacitive? Which color line corresponds to the circuit being inductive?

Here we have four sinusoidal lines plotted against time. And the three colored lines, which represent alternating current values, look pretty similar because they all have the same wavelength and amplitude. However, they have different phases, meaning their crests and troughs don’t perfectly match up with each other. And one place where all three lines are clearly distinguishable is here at the vertical axis, which represents time or 𝑡 equals zero. Here, the orange line has a positive value, the blue line has a zero value, and the red line has a negative value. And at 𝑡 equals zero, voltage, as represented by the black line, also equals zero.

Now, we wanna think about three circuits with different properties. So, for reference, let’s draw three circuit diagrams, each with an alternating current source connected to a single electrical component, either a resistor, capacitor, or inductor. Let’s first think about how voltage relates to the current of a resistive-only circuit. Recall that in an AC circuit that only includes a resistor, the circuit follows Ohm’s law, which states that voltage equals current times resistance. So, because voltage is directly proportional to current, they must be completely in phase with each other. Although they have different amplitudes, their crests and troughs match up. So if at any point voltage equals zero, we also know current equals zero. Looking back at the vertical axis, this corresponds to the blue line, which therefore represents the alternating current of a resistive-only circuit.

Next, let’s look at the circuit with the capacitor. Recall that as charge is driven through the circuit, equal and opposite charge accumulates on either side of the capacitor’s two plates, which creates a potential difference or voltage between the plates. Now, current causes this charge buildup. So it’s directly proportional to the change in potential difference between the plates over time. For instance, if there’s a negative value of current, that must mean there’s a negative change in voltage or that voltage is decreasing. Likewise, current will have a positive value when the voltage is increasing.

Looking back at 𝑡 equals zero, voltage has a positive slope, meaning its value is increasing. Therefore, the line that correctly represents current must have a positive value at that moment, which means it’s the orange line that corresponds to a capacitive circuit.

Finally, let’s consider an inductive circuit. Recall that current in an inductor creates a magnetic field. So when the current changes or alternates, the magnetic field also changes. This change in the magnetic field induces a potential difference and therefore a current to oppose that change. And the resulting potential difference is proportional to the change in current over time. So, at 𝑡 equals zero, voltage equals zero. And since voltage is proportional to the change in current, the correct current line should have a zero-valued slope or a horizontal slope at that moment. And then looking at the moments right after 𝑡 equals zero, say about here on the graph, voltage has a positive value, which must correspond to a positive slope or increasing value for current.

So, looking back at the graph, we can see that it’s the red line that has a horizontal slope at 𝑡 equals zero and a positive slope in the moments right after where voltage has a positive value. Therefore, the red line corresponds to an inductive circuit. And thus, we’ve explored the effects on voltage of alternating current circuits with several different electrical properties.

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