Explanation Given data: Refer to Figure 17.74(a) and 17.74(b) in the textbook. The inductor L is 1 H . Formula used: Write the general expression for Fourier series expansion. f ( t ) = a 0 + ∑ n = 1 ∞ a n cos n ω 0 t + ∑ n = 1 ∞ b n sin n ω 0 t (1) Write the expression to calculate the fundamental angular frequency. ω 0 = 2 π T (2) Here, T is the period of the function. Calculation: Refer to Figure 17.73(a) in the textbook. The source voltage v s ( t ) over the period is, f ( t ) = { 7 , 0 < t < 1 0 , 1 < t < 2 (3) The time period of Figure 17.17(a) is, T = 2 Substitute 2 for T in equation (2) to find the angular frequency ω 0 . ω 0 = 2 π 2 = π Finding the Fourier coefficient a 0 . a 0 = 1 T ∫ 0 T v s ( t ) d t (4) Applying equation (3) in equation (4) as follows, a 0 = 1 2 [ ∫ 0 1 7 d t + ∫ 1 2 0 d t ] { ∵ T = 2 } = 1 2 [ 7 [ t ] 0 1 + 0 ] = 1 2 [ 7 [ 1 − 0 ] ] = 7 2 Finding the Fourier coefficient a n . a n = 2 T ∫ 0 T v s ( t ) cos n ω 0 t d t (5) Applying equation (3) in equation (5) as follows, a n = 2 2 [ ∫ 0 1 ( 7 ) cos n π t d t + ∫ 1 2 ( 0 ) cos n π t d t ] { ∵ T = 2 , ω 0 = π } = 7 [ sin n π t n π ] 0 1 + 0 = 7 n π [ sin n π ( 1 ) − 0 ] = 7 n π [ sin n π ] The above equation becomes, a n = 0 { ∵ sin n π = 0 } Finding the Fourier coefficient b n . b n = 2 T ∫ 0 T v s ( t ) sin n ω 0 t d t (6) Applying equation (3) in equation (6) as follows, b n = 2 2 [ ∫ 0 1 ( 7 ) sin n π t d t + ∫ 1 2 ( 0 ) sin n π t d t ] { ∵ T = 2 , ω 0 = π } = 7 [ − cos n π t n π ] 0 1 + [ 0 ] = − 7 n π [ cos n π − cos n π ( 0 ) ] = − 7 n π [ cos n π − cos ( 0 ) ] Simplify the equation as follows, b n = − 7 n π [ cos n π − 1 ] { ∵ cos ( 0 ) = 1 } = 7 n π [ 1 − cos n π ] = 7 n π [ 1 − cos n ω ] { ∵ ω = π } = 7 n π [ 1 − ( − 1 ) n ] { ∵ cos n ω = ( − 1 ) n } The above equation becomes, b n = { 14 n π , n = odd 0, n = even (7) Substituting the Fourier coefficients in equation (1) as follows, v s ( t ) = 7 2 + ∑ n = 1 ∞ ( 0 ) cos n ω 0 t + 14 π ∑ k = 1 ∞ 1 n sin n π t , n = 2 k + 1 { ω 0 = π } v s ( t ) = 3

6th Edition

ISBN: 9780078028229

Author: Charles K Alexander, Matthew Sadiku

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Fourier Series

Most of the incidents studied in the field of Engineering and Science as a function of time. For example, current and voltage are in the alternating current circuit. These occasional activities can be analyzed in the activity components (fundamental freq…

Videos

Question

Chapter 17, Problem 38P

To determine

Find the voltage across the inductor vo(t) of the circuit shown in Figure 17.74(b).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17, Problem 37P

Chapter 17, Problem 39P

Students have asked these similar questions

5052 ми a JXL 000 +2 16s (wt) bi jxc M 100♫ ZL. Find the Value of XL & X c if the Circuit trans for Max. Power to (ZL).

Choose the best answer for each: 1. What does SRAM use to store data? 。 a) Capacitors ob) Latches 。 c) Flip-flops od) Transistors 2. Which RAM type requires refreshing? o a) SRAM ob) DRAM 。 c) ROM od) Flash 3. What type of memory retains data only while power is on? a) ROM 。 b) EEPROM o c) DRAM od) Flash 4. How many addresses can a 15-bit address bus handle? o a) 32k • b) 64k o c) 16k od) lk 5. What operation occurs when data is copied out of memory without erasing? oa) Write ob) Read o c) Refresh o d) Load 6. DRAM cells store bits using: a) Flip-flops 。 b) Capacitors c) Diodes od) Resistors 7. The cache located inside the CPU is: 。 a) L2 cache o b) LI cache °c) ROM od) HDD 8. SDRAM is synchronized with: o a) Cache ob) Data Bus c) System Clock od) Hard Disk 9. The bus that carries commands is called: o a) Data Bus b) Control Bus o c) Address Bus o d) Logic Bus 10. What is the main use of SRAM? o Disk storage o Cache o Main memory o Registers 11. The smallest addressable unit in…

Q4: A cache memory is 128k × 16. How many bytes can it store?

Chapter 17 Solutions

Fundamentals of Electric Circuits

Ch. 17.2 - Find the Fourier series of the square wave in Fig....Ch. 17.2 - Determine the Fourier series of the sawtooth...Ch. 17.3 - Prob. 3PP Ch. 17.3 - Find the Fourier series expansion of the function...Ch. 17.3 - Prob. 5PP Ch. 17.4 - Prob. 6PP Ch. 17.4 - If the input voltage in the circuit of Fig. 17.24...Ch. 17.5 - The voltage and current at the terminals of a...Ch. 17.5 - Find the rms value of the periodic current i(t) =...Ch. 17.6 - Obtain the complex Fourier series of the function...

Ch. 17.6 - Obtain the complex Fourier series expansion of...Ch. 17.7 - Prob. 12PP Ch. 17.8 - Rework Example 17.14 if the low-pass filter is...Ch. 17 - Which of the following cannot be a Fourier series?...Ch. 17 - If ft=t,0t,ft+n=ft, the value of 0 is (a) 1 (b) 2...Ch. 17 - Which of the following are even functions? (a) t +...Ch. 17 - Prob. 4RQ Ch. 17 - Prob. 5RQ Ch. 17 - If f(t) = 10 + 8 cos t + 4 cos 3t + 2 cos 5t + ,...Ch. 17 - Prob. 7RQ Ch. 17 - The plot of |cn| versus n0 is called: (a) complex...Ch. 17 - Prob. 9RQ Ch. 17 - Prob. 10RQ Ch. 17 - Evaluate each of the following functions and see...Ch. 17 - Using MATLAB, synthesize the periodic waveform for...Ch. 17 - Given that Fourier coefficients a0, an, and bn of...Ch. 17 - Find the Fourier series expansion of the backward...Ch. 17 - Prob. 5P Ch. 17 - Find the trigonometric Fourier series for f t =...Ch. 17 - Determine the Fourier series of the periodic...Ch. 17 - Using Fig. 17.51, design a problem to help other...Ch. 17 - Determine the Fourier coefficients an and bn of...Ch. 17 - Find the exponential Fourier series for the...Ch. 17 - Obtain the exponential Fourier series for the...Ch. 17 - Prob. 12P Ch. 17 - Prob. 13P Ch. 17 - Find the quadrature (cosine and sine) form of the...Ch. 17 - Express the Fourier series...Ch. 17 - The waveform in Fig. 17.55(a) has the following...Ch. 17 - Prob. 17P Ch. 17 - Prob. 18P Ch. 17 - Obtain the Fourier series for the periodic...Ch. 17 - Prob. 20P Ch. 17 - Prob. 21P Ch. 17 - Calculate the Fourier coefficients for the...Ch. 17 - Using Fig. 17.61, design a problem to help other...Ch. 17 - Prob. 24P Ch. 17 - Determine the Fourier series representation of the...Ch. 17 - Find the Fourier series representation of the...Ch. 17 - For the waveform shown in Fig. 17.65 below, (a)...Ch. 17 - Obtain the trigonometric Fourier series for the...Ch. 17 - Prob. 29P Ch. 17 - Prob. 30P Ch. 17 - Prob. 31P Ch. 17 - Prob. 32P Ch. 17 - Prob. 33P Ch. 17 - Prob. 34P Ch. 17 - Prob. 35P Ch. 17 - Prob. 36P Ch. 17 - If the periodic current waveform in Fig. 17.73(a)...Ch. 17 - Prob. 38P Ch. 17 - Prob. 39P Ch. 17 - The full-wave rectified sinusoidal voltage in Fig....Ch. 17 - Prob. 42P Ch. 17 - The voltage across the terminals of a circuit is...Ch. 17 - Prob. 44P Ch. 17 - A series RLC circuit has R = 10 , L = 2 mH, and C...Ch. 17 - Prob. 46P Ch. 17 - Prob. 47P Ch. 17 - Prob. 48P Ch. 17 - Prob. 49P Ch. 17 - Prob. 50P Ch. 17 - Prob. 51P Ch. 17 - Prob. 52P Ch. 17 - Prob. 53P Ch. 17 - Find the exponential Fourier series for the...Ch. 17 - Obtain the exponential Fourier series expansion of...Ch. 17 - The Fourier series trigonometric representation of...Ch. 17 - Prob. 57P Ch. 17 - Find the exponential Fourier series of a function...Ch. 17 - Prob. 59P Ch. 17 - Obtain the complex Fourier coefficients of the...Ch. 17 - The spectra of the Fourier series of a function...Ch. 17 - Prob. 62P Ch. 17 - Plot the amplitude spectrum for the signal f2(t)...Ch. 17 - Prob. 64P Ch. 17 - Prob. 65P Ch. 17 - Prob. 66P Ch. 17 - Prob. 67P Ch. 17 - Prob. 68P Ch. 17 - Prob. 69P Ch. 17 - Design a problem to help other students better...Ch. 17 - Prob. 71P Ch. 17 - Prob. 72P Ch. 17 - Prob. 73P Ch. 17 - Prob. 74P Ch. 17 - Prob. 75P Ch. 17 - Prob. 76P Ch. 17 - Prob. 77CP Ch. 17 - Prob. 78CP Ch. 17 - Consider the full-wave rectified sinusoidal...Ch. 17 - Prob. 82CP

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Find the voltage across the inductor v o ( t ) of the circuit shown in Figure 17.74(b).

Solution Summary: The author shows the voltage across the inductor v_o(t) of the circuit shown in Figure 17.74.

Concept explainers

Videos

Find the voltage across the inductor vo(t) of the circuit shown in Figure 17.74(b).

Want to see the full answer?

Chapter 17 Solutions