Concept explainers
For the circuit shown in Fig. 2.116, find the equivalent resistance. All resistors are 3Ω.
Figure 2.116
Calculate the equivalent resistance to the circuit connection in Figure 2.116.
Answer to Problem 52P
The equivalent resistance to the circuit connection in Figure 2.116 is
Explanation of Solution
Formula used:
Consider the following delta to wye conversion, when all branches in a delta consist same value.
Consider the expression for
Here,
Consider the expression for
Calculation:
Refer to Figure 2.116 in the textbook For Prob.2.52.
Step 1:
In Figure 2.116, convert the wye- sub network at right side top corner connection into delta connection.
Substitute
Since all branches values are same in a wye connection that is
Step 2:
In Figure 2.116, as two
Modify Figure 2.116 as shown in Figure 1.
Step 3:
In Figure 1, as
Step 4:
In Figure 1,
Modify Figure 1 as shown in Figure 2.
Step 5:
In Figure 2, as
Modify Figure 2 as shown in Figure 3.
Step 6:
In Figure 3,
Step 7:
In Figure 3,
Modify Figure 3 as shown in Figure 4.
Step 8:
In Figure 4, as
Modify Figure 4 as shown in Figure 5.
Step 9:
In Figure 5,
Modify Figure 5 as shown in Figure 6.
Step 10:
In Figure 6, as
Conclusion:
Thus, the equivalent resistance to the circuit connection in Figure 2.116 is
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