(a) Explanation Given Data: The given function is as follows, y ( t ) = 4 sin 2 t (1) Values of t are 0 , 0.001 , 0.01 , 0.1 and 1 . Calculation: A linear function is a simple function composed of constant terms and simple variable without exponent. When argument of sine function is close to zero then sine function behaves as linear function and now value of linear function is equal to its argument. So linear approximation of function y ( t ) is as follows, y ( t ) l i n e a r ≈ 4 ( 2 t ) y ( t ) l i n e a r = 8 t (2) The expression for percentage change in given function is as follows, Δ y ( t ) = y ( t ) l i n e a r − y ( t ) y ( t ) × 100 (3) Here, Δ y ( t ) is percentage change in given function, y ( t ) is given function and y ( t ) l i n e a r is linear approximation f function. For t = 0 , Substitute 0 for t in equation (1), y ( 0 ) = 4 sin 2 ( 0 ) = 4 sin 0 = 4 ( 0 ) = 0 Substitute 0 for t in equation (2), y ( 0 ) l i n e a r = 8 ( 0 ) = 0 As value of y ( 0 ) l i n e a r is equal to value of y ( 0 ) . which means percentage change in the value of function is 0 . For t = 0.001 , Substitute 0.001 for t in equation (1), y ( 0.001 ) = 4 sin 2 ( 0.001 ) = 4 sin 0.002 = 4 ( 0.00199 ) = 0.00799 Substitute 0.001 for t in equation (2), y ( 0.001 ) l i n e a r = 8 ( 0.001 ) = 0.008 Substitute 0.00799 for y ( 0.001 ) and 0.008 for y ( 0.001 ) l i n e a r in equation (3), Δ y ( 0.001 ) = 0.008 − 0.00799 0.00799 × 100 = 0.00001 0.00799 × 100 = 0.125 % So percentage change in given function for t = 0.001 is 0.125 % . For t = 0.01 , Substitute 0.01 for t in equation (1), y ( 0.01 ) = 4 sin 2 ( 0.01 ) = 4 sin 0.02 = 4 ( 0.0199 ) = 0.0799 Substitute 0 (b) To determine For which values of t value of linear function is approximately equal to y ( t ) .

Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf

9th Edition

ISBN: 9781259989452

Author: Hayt

Publisher: Mcgraw Hill Publishers

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Chapter 5, Problem 2E

(a)

To determine

Evaluate linear function for given values of t.

(b)

To determine

For which values of t value of linear function is approximately equal to y(t).

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Chapter 5, Problem 1E

Chapter 5, Problem 3E

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Chapter 5 Solutions

Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf

Ch. 5.1 - For the circuit of Fig. 5.4, use superposition to...Ch. 5.2 - For the circuit of Fig. 5.7, use superposition to...Ch. 5.2 - For the circuit of Fig. 5.18, compute the current...Ch. 5.2 - For the circuit of Fig. 5.20, compute the voltage...Ch. 5.3 - Using repeated source transformations, determine...Ch. 5.3 - Use Thvenins theorem to find the current through...Ch. 5.3 - Determine the Thvenin and Norton equivalents of...Ch. 5.3 - Find the Thvenin equivalent for the network of...Ch. 5.3 - Find the Thvenin equivalent for the network of...Ch. 5.4 - Consider the circuit of Fig. 5.43. FIGURE 5.43...

Ch. 5.5 - Prob. 11P Ch. 5 - Linear systems are so easy to work with that...Ch. 5 - Prob. 2E Ch. 5 - Prob. 3E Ch. 5 - (a) Employ superposition to determine the current...Ch. 5 - (a) Using superposition to consider each source...Ch. 5 - (a) Determine the individual contributions of each...Ch. 5 - (a) Determine the individual contributions of each...Ch. 5 - After studying the circuit of Fig. 5.53, change...Ch. 5 - Consider the three circuits shown in Fig. 5.54....Ch. 5 - (a) Using superposition, determine the voltage...Ch. 5 - Employ superposition principles to obtain a value...Ch. 5 - (a) Employ superposition to determine the...Ch. 5 - Perform an appropriate source transformation on...Ch. 5 - (a) For the circuit of Fig. 5.59, plot iL versus...Ch. 5 - Determine the current labeled I in the circuit of...Ch. 5 - Verify that the power absorbed by the 7 resistor...Ch. 5 - (a) Determine the current labeled i in the circuit...Ch. 5 - (a) Using repeated source transformations, reduce...Ch. 5 - Prob. 19E Ch. 5 - (a) Making use of repeated source transformations,...Ch. 5 - Prob. 21E Ch. 5 - (a) With the assistance of source transformations,...Ch. 5 - For the circuit in Fig. 5.67 transform all...Ch. 5 - Prob. 24E Ch. 5 - (a) Referring to Fig. 5.69, determine the Thevenin...Ch. 5 - (a) With respect to the circuit depicted in Fig....Ch. 5 - (a) Obtain the Norton equivalent of the network...Ch. 5 - (a) Determine the Thevenin equivalent of the...Ch. 5 - Referring to the circuit of Fig. 5.71: (a)...Ch. 5 - Prob. 30E Ch. 5 - (a) Employ Thvenins theorem to obtain a...Ch. 5 - Prob. 32E Ch. 5 - Determine the Norton equivalent of the circuit...Ch. 5 - For the circuit of Fig. 5.75: (a) Employ Nortons...Ch. 5 - (a) Obtain a value for the Thvenin equivalent...Ch. 5 - Prob. 36E Ch. 5 - Obtain a value for the Thvenin equivalent...Ch. 5 - With regard to the network depicted in Fig. 5.79,...Ch. 5 - Determine the Thvenin and Norton equivalents of...Ch. 5 - Determine the Norton equivalent of the circuit...Ch. 5 - Prob. 41E Ch. 5 - Determine the Thvenin and Norton equivalents of...Ch. 5 - Prob. 43E Ch. 5 - Prob. 44E Ch. 5 - Prob. 45E Ch. 5 - (a) For the simple circuit of Fig. 5.87, find the...Ch. 5 - For the circuit drawn in Fig. 5.88, (a) determine...Ch. 5 - Study the circuit of Fig. 5.89. (a) Determine the...Ch. 5 - Prob. 49E Ch. 5 - Prob. 50E Ch. 5 - With reference to the circuit of Fig. 5.91, (a)...Ch. 5 - Prob. 52E Ch. 5 - Select a value for RL in Fig. 5.93 such that it...Ch. 5 - Determine what value of resistance would absorb...Ch. 5 - Derive the equations required to convert from a...Ch. 5 - Convert the - (or "-") connected networks in Fig....Ch. 5 - Convert the Y-(or T-) connected networks in Fig....Ch. 5 - For the network of Fig. 5.97, select a value of R...Ch. 5 - For the network of Fig. 5.98, select a value of R...Ch. 5 - Prob. 60E Ch. 5 - Calculate Rin as indicated in Fig.5.100. FIGURE...Ch. 5 - Employ Y conversion techniques as appropriate to...Ch. 5 - Prob. 63E Ch. 5 - (a) Use appropriate techniques to obtain both the...Ch. 5 - (a) For the network in Fig. 5.104, replace the...Ch. 5 - Prob. 66E Ch. 5 - Prob. 67E Ch. 5 - A 2.57 load is connected between terminals a and...Ch. 5 - A load resistor is connected across the open...Ch. 5 - A backup is required for the circuit depicted in...Ch. 5 - (a) Explain in general terms how source...Ch. 5 - The load resistor in Fig. 5.108 can safely...Ch. 5 - Prob. 74E Ch. 5 - As part of a security system, a very thin 100 ...Ch. 5 - With respect to the circuit in Fig. 5.90, (a)...

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