Resolved Problems about Electrical Resistance

Problem 2.11 Source: Problem elaborated by the author of the site.

Calculate the equivalent resistance between the points x-y of the circuit shown in Figure 02-11.1.

Solution of the Problem 2.11

In the circuit above the nodes were enumerated for a better understanding of the solution. Since the circuit is fully symmetrical, let's assume that at point x enters a current of value I. Thus, by calculating the potential difference between the points x-y and dividing by the current I, we find the value of the equivalent circuit resistance between these points.

From the circuit you can see that:

V_xy = V_ea + V_ad + V_dc

From the symmetry of the circuit, we easily conclude that between the points and -a will circulate a current of value I / 3 . Then it is possible to calculate the potential difference between the points e-a, or:

V_ea = R (I / 3 )

I / 3

point a

points a-d

I / 6

I / 3

V_ad = R (I / 6 )

And by the resistance that is between the points d-c , will circulate a current equal to I / 3 , which is the sum of the currents I_ad + I_hd = I/6 + I/6 = I/3. Then:

V_dc = R (I / 3 )

Now we have all potential differences calculated. So just add them up and we'll find:

V_xy = R (I/3) + R (I/6) + R (I/3) = I ( 5 R / 6 )

And, as stated earlier, dividing V_xy by the value of I gives us the equivalent resistance between points xy, or:

R_xy = 5 R / 6

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