Question

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Four resistors of 4 ohm each are joined end to end to form a square. Calculate the equivalent resistance of the combination between two adjacent corner??

Answer 1

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Answer 2

Given,

4 resistors are joined end to end to form a square.

Resistance of each resistor = 4 ohms

To find,

The equivalent resistance of the combination between two adjacent corners.

Solution,

We can simply solve this numerical problem by using the following process:

Mathematically,

If a set of resistors are arranged in a series type of arrangement, then the equivalent resistance of the arrangement is equal to the total of the individual resistances. Similarly, if a set of resistors are arranged in a parallel type of arrangement, then the reciprocal of the equivalent resistance of the arrangement is equal to the sum of the reciprocals of the individual resistances.

As per the question;

The 4 given resistors are connected in a square form such that, between its two adjacent corners, a set of 3 resistors, arranged in a series type of arrangement, is connected to the fourth resistor in a parallel type of arrangement.

Now,

the equivalent resistance of the set of 3 resistors, arranged in a series type of arrangement

= 4 ohms + 4 ohms + 4 ohms

= 12 ohms

The equivalent resistance of the parallel type (R) of arrangement can be calculated as follows;

=> 1/R = 1/12 + 1/4 = 4/12 = 1/3

=> R = 3 ohms

Hence, the equivalent resistance of the combination, between two adjacent corners, is equal to 3 ohms.