Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
Question
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Chapter 13, Problem 1E

(a)

To determine

Find the steady-state expression for v1 when i1=0A and i2=5cos(8t)A.

(a)

Expert Solution
Check Mark

Answer to Problem 1E

The steady-state expression for v1 is 0.04sin(8t)V_.

Explanation of Solution

Given data:

Refer to Figure 13.35 in the textbook for the given circuit.

L1=10mHL2=5mHM=1mH

i1=0Ai2=5cos(8t)A

Formula used:

Write the expression for steady-state expression for v1 in the given circuit as follows:

v1=L1di1dt+Mdi2dt        (1)

Here,

L1 is the self-inductance of primary coil and

M is the mutual inductance of the primary and secondary coils.

Calculation:

Substitute 10mH for L1, 1mH for M, 0 A for i1, and 5cos(8t)A for i2 in Equation (1) to obtain the steady-state expression for v1.

v1=(10mH)[ddt(0A)]+(1mH)[ddt(5cos(8t)A)]=0V+[(1×103)(5)(8)sin(8t)]V=0.04sin(8t)V

Conclusion:

Thus, the steady-state expression for v1 is 0.04sin(8t)V_.

(b)

To determine

Find the steady-state expression for v2 when i1=3sin(100t)A and i2=0A.

(b)

Expert Solution
Check Mark

Answer to Problem 1E

The steady-state expression for v2 is 0.3cos(100t)V_.

Explanation of Solution

Given data:

L2=5mHi1=3sin(100t)Ai2=0A

Formula used:

Write the expression for steady-state expression for v2 in the given circuit as follows:

v2=L2di2dt+Mdi1dt        (2)

Here,

L2 is the self-inductance of secondary coil.

Calculation:

Substitute 5mH for L2, 1mH for M, 3sin(100t)A for i1, and 0 A for i2 in Equation (2) to obtain the steady-state expression for v2.

v2=(5mH)[ddt(0A)]+(1mH)[ddt(3sin(100t)A)]=0V+[(1×103)(3)(100)cos(100t)]V=0.3cos(100t)V

Conclusion:

Thus, the steady-state expression for v2 is 0.3cos(100t)V_.

(c)

To determine

Find the steady-state expression for v2 when i1=5cos(8t40°)A and i2=4sin(8t)A.

(c)

Expert Solution
Check Mark

Answer to Problem 1E

The steady-state expression for v2 is 0.16cos(8t)0.04sin(8t40°)V_.

Explanation of Solution

Given data:

i1=5cos(8t40°)Ai2=4sin(8t)A

Calculation:

Substitute 5mH for L2, 1mH for M, 5cos(8t40°)A for i1, and 4sin(8t)A for i2 in Equation (2) to obtain the steady-state expression for v2.

v2=(5mH)[ddt(4sin(8t)A)]+(1mH)[ddt(5cos(8t40°)A)]=[(5×103)(4)(8)cos(8t)]V+[(1×103)(5)(8)sin(8t40°)]V=0.16cos(8t)0.04sin(8t40°)V

Conclusion:

Thus, the steady-state expression for v2 is 0.16cos(8t)0.04sin(8t40°)V_.

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Chapter 13 Solutions

Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf

Ch. 13 - With respect to Fig. 13.36, assume L1 = 500 mH, L2...Ch. 13 - The circuit in Fig. 13.36 has a sinusoidal input...Ch. 13 - Prob. 4ECh. 13 - Prob. 5ECh. 13 - The circuit in Fig. 13.38 has a sinusoidal input...Ch. 13 - The physical construction of three pairs of...Ch. 13 - Prob. 8ECh. 13 - Prob. 9ECh. 13 - Calculate v1 and v2 if i1 = 5 sin 40t mA and i2 =...Ch. 13 - Prob. 11ECh. 13 - For the circuit of Fig. 13.41, calculate I1, I2,...Ch. 13 - Prob. 13ECh. 13 - Prob. 14ECh. 13 - In the circuit of Fig. 13.43, M is reduced by an...Ch. 13 - Prob. 16ECh. 13 - Prob. 17ECh. 13 - Prob. 18ECh. 13 - Prob. 19ECh. 13 - Note that there is no mutual coupling between the...Ch. 13 - Prob. 21ECh. 13 - (a) Find Zin(j) for the network of Fig 13.50. (b)...Ch. 13 - For the coupled coils of Fig. 13.51, L1 = L2 = 10...Ch. 13 - Prob. 24ECh. 13 - Prob. 25ECh. 13 - Prob. 26ECh. 13 - Consider the circuit represented in Fig. 13.53....Ch. 13 - Compute v1, v2, and the average power delivered to...Ch. 13 - Assume the following values for the circuit...Ch. 13 - Prob. 30ECh. 13 - Prob. 31ECh. 13 - Prob. 32ECh. 13 - Prob. 33ECh. 13 - Prob. 34ECh. 13 - Prob. 35ECh. 13 - Prob. 36ECh. 13 - Prob. 37ECh. 13 - FIGURE 13.60 For the circuit of Fig. 13.60, redraw...Ch. 13 - Prob. 39ECh. 13 - Prob. 40ECh. 13 - Calculate the average power delivered to the 400 m...Ch. 13 - Prob. 42ECh. 13 - Calculate the average power delivered to each...Ch. 13 - Prob. 44ECh. 13 - Prob. 45ECh. 13 - Prob. 46ECh. 13 - Prob. 47ECh. 13 - Prob. 48ECh. 13 - A transformer whose nameplate reads 2300/230 V, 25...Ch. 13 - Prob. 52ECh. 13 - As the lead singer in the local rock band, you...Ch. 13 - Obtain an expression for V2/Vs in the circuit of...Ch. 13 - Prob. 55E
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