Concept explainers
Obtain the equivalent resistance at the terminals a-b for each of the circuits in Fig. 2.115.
Figure 2.115
(a)
Calculate the equivalent resistance at terminals a-b in Figure 2.115(a).
Answer to Problem 51P
The equivalent resistance at terminals a-b in Figure 2.115(a) is
Explanation of Solution
Formula used:
Consider the following delta to wye conversion, when all branches in a delta consists same value.
Consider the expression for
Here,
Consider the expression for
Calculation:
Refer to Figure 2.115(a) in the textbook For Prob.2.51.
Step 1:
In Figure 2.115(a), convert the wye connection into delta connection.
Substitute
Since all branches values are same in a wye connection that is
Modify Figure 2.115(a) as shown in Figure 1.
Step 2:
In Figure 1, as
Step 3:
In Figure 1, as
Step 4:
In Figure 1, as
Modify Figure 1 as shown in Figure 2.
Step 5:
In Figure 2, as two
Modify Figure 2 as shown in Figure 3.
Step 6:
In Figure 3, as
Conclusion:
Thus, the equivalent resistor at terminals a-b in Figure 2.115(a) is
(b)
Calculate the equivalent resistance at terminals a-b in Figure 2.115(b).
Answer to Problem 51P
The equivalent resistance at terminals a-b in Figure 2.115(b) is
Explanation of Solution
Formula used:
Consider the wye to delta conversions.
Here,
Calculation:
Refer to Figure 2.115(b) in the textbook For Prob.2.51.
Step 1:
In Figure 2.115(a), convert the wye connection
Consider
Substitute
Substitute
Substitute
Modify Figure 2.115(b) as shown in Figure 4.
Step 2:
In Figure 4, as
Step 3:
In Figure 4, as
Modify Figure 4 as shown in Figure 5.
Step 4:
In Figure 5, as
Modify Figure 5 as shown in Figure 6.
Step 5:
In Figure 6, as
Conclusion:
Thus, the equivalent resistor at terminals a-b in Figure 2.115(b) is
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