Question Video: Identifying Equivalent Circuit Diagrams Physics • 9th Grade

Are the two circuits shown in the diagram equivalent?

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Video Transcript

Are the two circuits shown in the diagram equivalent?

In this question, we are presented with two circuits, and we need to find out if these two circuits are equivalent. In the right circuit, we have a cell and a single resistor with a resistance of 300 ohms. In the left circuit, we have a cell and two resistors that are connected in series.

To compare these two circuits, we need to compare their total resistances. If both circuits have the same total resistance, then they will be equivalent to each other. The circuit on the right only contains a single resistor, so the total resistance of this circuit is 300 ohms. The circuit on the left contains two resistors connected in series. To find the total resistance of the circuit, we need to find the total resistance of the combination of resistors.

We can recall that for any number of resistors in series, the total resistance, 𝑅 total, equals 𝑅 one plus 𝑅 two plus and so on plus 𝑅 sub 𝑁. Since there are two resistors connected in series in the left circuit, this formula simplifies to 𝑅 left equals 𝑅 one plus 𝑅 two. One resistor has a resistance of 120 ohms, and the other resistor has a resistance of 240 ohms. So, 𝑅 left will equal 120 ohms plus 240 ohms, which equals 360 ohms. So we have found that the left circuit in the question, which contains two resistors connected in series, is equivalent to a circuit containing a single resistor with a resistance of 360 ohms.

If we compare this equivalent circuit to the right circuit in the question, we can see that the circuits are different. Both circuits now contain a cell and a single resistor. However, the resistances of the resistors have different values. The left circuit has a total resistance of 360 ohms; meanwhile, the right circuit has a total resistance of 300 ohms.

Therefore, the answer is no. The two circuits shown in the diagram are not equivalent.