Concept explainers
In the circuit of Fig. 13.43, M is reduced by an order of magnitude. Calculate i3 if v1 = 10 cos (800t − 20°) V.
FIGURE 13.43
Find the value of
Answer to Problem 15E
The value of
Explanation of Solution
Given data:
Refer to Figure 13.43 in the textbook for the given circuit.
The value of mutual inductance is reduced by an order of magnitude. Therefore, write the value of mutual inductance as follows:
Formula used:
Write the expression for reactance due to self-inductance as follows:
Here,
Write the expression for reactance due to capacitance as follows:
Here,
Write the expression for reactance due to mutual-inductance as follows:
Here,
Calculation:
From the given source voltage, write the value of angular frequency and the source voltage
Rewrite the expression for
Substitute
Substitute
Substitute
Substitute
Use the obtained values of reactance due to inductor and capacitors and draw the phasor representation for the given circuit as shown in Figure 1.
Apply KVL to the loop-
Neglect the dimensions and write the expression as follows:
Apply KVL to the loop-
Apply KVL to the loop-
Neglect the dimensions and write the expression as follows:
From the circuit in Figure 1, write the expression for
From the circuit in Figure 1, write the expression for
Rewrite the expression in Equation (4) as follows:
Substitute
Simplify the expression as follows:
Rearrange the expression in Equation (6) as follows:
Substitute
Simplify the expression as follows:
From Equation (9), substitute
Simplify the expression as follows:
Substitute
Simplify the expression as follows:
Rearrange the expression in Equation (5) as follows:
Substitute
From Equation (11), substitute
Simplify the expression as follows:
Substitute
Simplify the expression as follows;
Rewrite the expression in polar form to obtain the value of
Conclusion:
Thus, the value of
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Chapter 13 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
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