Calculate the equivalent resistance Req of the network shown in Fig. 3.87 if R1 = 2R2 = 3R3 = 4R4 etc. and R11 = 3

The equivalent resistance of the network shown is:

So, first of all, we can start by determining what each of the resistances is equal to. In this case we can start by saying that This means that:

Therefore:

We can now use this value to find the value of the other resistances. The given condition for the resistances can be represented with the following formula:

so:

So now that we know what each resistance is equal to, we can go ahead and analyze the circuit.

In this case we can see that and are parallel, so we can calculate their equivalent resistance.

Which yields:

Now, , and are connected in series, so we can calculate their equivalent resistance like this:

Now,  we can see that and are parallel, so we can calculate their equivalent resistance.

Which yields:

Now, , and are connected in series, so we can calculate their equivalent resistance like this:

Next,  we can see that and are parallel, so we can calculate their equivalent resistance.

Which yields:

Now, , and are connected in series, so we can calculate their equivalent resistance like this:

Finally, we can see that and are parallel, so we can calculate their equivalent resistance.

Which yields:

See attached picture for images on how to reduce the circuit.

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