(a) Explanation Given data: The circuit diagram is given in Figure 17.80. The value of resistance ( R ) is 2 k Ω . The value of capacitor is 100 μ F . The applied current is, i ( t ) = 20 + 16 cos ( 10 + 45 ° ) + 12 cos ( 20 t − 60 ° ) mA (1) Formula used: Write the Ohm’s law formula to find the voltage. V = I R (2) Here, V is the voltage, I is the current, and R is the resistance. Write the expression for capacitive impedance. Z c = 1 j ω n C (3) Here, C is the capacitor, and ω n is the frequency. Write the general expression for voltage in amplitude-phase form. v ( t ) = V dc + ∑ n = 1 ∞ V n cos ( n ω 0 t − θ n ) (4) Here, V dc is the DC component of voltage, V n is the AC component of voltage, n is the number of components, ω 0 is the frequency, and θ n is the phase angle between the voltages. Write the general expression for current in amplitude-phase form. i ( t ) = I dc + ∑ m = 1 ∞ I m cos ( m ω 0 t − ϕ m ) (5) Here, I dc is the DC component of current, I m is the AC component of current, m is the number of components, ω 0 is the frequency, and ϕ m is the phase angle between the currents. Calculation: Expand the equation (5) as follows. i ( t ) = I dc + ∑ m = 1 2 I m cos ( m ω 0 t − ϕ m ) i ( t ) = I dc + I 1 cos ( ω 0 t − ϕ 1 ) + I 2 cos ( 2 ω 0 t − ϕ 2 ) (6) Compare equations (1) and (6). I dc = 20 mA I 1 = 16 mA I 2 = 12 mA ω 0 = 10 In the given figure, while calculating the DC component values, the capacitor acts like an open circuit. Therefore, DC voltage depends upon the value of current and resistor. Modify equation (2) to find V dc . V dc = I dc R Substitute 2 k Ω for R and 20 mA for I dc to find V dc . V dc = ( 20 mA ) ( 2 k Ω ) = ( 20 × 10 − 3 A ) ( 2 × 10 3 Ω ) { ∵ 1 mA = 1 × 10 − 3 A ∵ 1 k Ω = 1 × 10 3 Ω } = 40 V Find the value of AC component of voltages. Write the expression for ω n . ω n = m ω 0 Substitute 10 for ω 0 . ω n = 10 m Substitute 10 m for ω n and 100 μ F for C in equation (3) to find capacitive impedance. Z c = 1 j ( 10 m ) ( 100 μ F ) = 1 j ( 10 m ) ( 100 × 10 − 6 F ) { ∵ 1 μ F = 1 × 10 − 6 F } = 1 j 0.001 m Z c = ( 1 j m ) k Ω In the given figure, capacitor and resistor are connected in parallel combination. Find the total impedance of the circuit. Z m = R ∥ Z c Substitute 2 k Ω for R and ( 1 j m ) Ω for Z c to find Z . Z m = ( 2 k Ω ) ∥ ( ( 1 j m ) k Ω ) = ( 2 k Ω ) ( ( 1 j m ) k Ω ) ( 2 k Ω ) + ( ( 1 j m ) k Ω ) = ( 2 j ) ( 2 + 1 j m ) Ω = ( − j 2 m ) ( 2 − j m ) Ω Simplify the expression as follows (b) To determine Find the value of average power dissipated in the resistor.

Loose Leaf for Fundamentals of Electric Circuits Format: LooseLeaf

6th Edition

ISBN: 9781259657054

Author: Alexander

Publisher: Mcgraw Hill Publishers

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Fourier Transform

In mathematics, the Fourier transformation is a mathematical transformation that rotates responsibilities by using region or time into tasks depending on the local or temporal frequency, such as the rendering of a musical track in step with existing volu…

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Chapter 17, Problem 48P

(a)

To determine

Find the value of v(t) for the circuit given in Fig 17.80.

(b)

To determine

Find the value of average power dissipated in the resistor.

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Chapter 17, Problem 47P

Chapter 17, Problem 49P

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Chapter 17 Solutions

Loose Leaf for Fundamentals of Electric Circuits Format: LooseLeaf

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

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Find the value of v ( t ) for the circuit given in Fig 17.80.

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Find the value of v(t) for the circuit given in Fig 17.80.

Find the value of average power dissipated in the resistor.

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Chapter 17 Solutions