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.
