Worked examples

WORKED EXAMPLES

Example 1 For the passive circuit consisting of resistances (in ohms) as shown, calculate the equivalent resistance between the terminals A and D.

Solution: Between the terminals A and D in the circuit given, the combination is neither series nor parallel. Hence, simplification is not possible as it is. So, we can convert the delta between A, B and C into equivalent star. As a result, the circuit becomes as drawn below:

Now, it is series parallel combination of resistances. Hence the total resistance between A and D is equal to

Example 2 For the network shown in the figure below, find the equivalent resistance between the terminals B and C.

Solution: The given combination of resistances between the terminals B and C is neither series combination nor parallel combination. If, the star connection between A, B and C is converted into equivalent delta, we will have a known combination which can be simplified by series parallel simplification.

The given figure is re-drawn after replacing the star by its equivalent Delta.

The resistance between B and C terminals is equivalent to the parallel combination of 3 and 1.5 ohms.

Example 3 Determine the equivalent resistance between A and B.

Solution: The combination is neither series nor parallel. There is delta and star connection. Converting the star connection for which N is the star point and re-drawing the circuit, we get

Example 4 Determine the equivalent resistance across AB of the circuit shown in the figure wallet to da od sto od stolwo in below.

Solution: None of the resistances in the circuit are connected in known fashion. There are formations of deltas and stars as observed. Let us convert the inner delta into equivalent star. In the equivalent star the value of each resistance will be 6/3 = 2Ω this conversion, we get the following circuit.

In the above figure, converting the inner star into its equivalent delta and re-drawing the circuit, we get the following figure.