Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN: 9781133939146
Author: Katz, Debora M.
Publisher: Cengage Learning
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Chapter 33, Problem 59PQ

(a)

To determine

The total resistance of the circuit.

(a)

Expert Solution
Check Mark

Answer to Problem 59PQ

The total resistance is 8.41Ω.

Explanation of Solution

Write the expression to calculate the voltage across the AC generator.

    ε(t)=VL(t)+VR(t)+VC(t)                                                                                  (I)

Here, ε is the total voltage across the AC generator, VL the voltage across the inductor, VC is the voltage across the capacitor and VR is the voltage across the resistor.

Write the expression for voltage across the generator

    ε(t)=εmaxsin(ωt+ϕ)

Here, εmax is the maximum voltage, ω is the angular frequency and ϕ is the phase angle.

Write the expression for voltage across the inductor.

    VL(t)=XLImaxsin(ωt+π2)

Here, Imax is the maximum current in the inductor and XL is the inductive reactance.

Write the expression for voltage across the capacitor.

    VC(t)=XCImaxsin(ωt+π2)

Here, the capacitive reactance is XC

Write the expression for the voltage across the resistor.

    VR(t)=RImaxsin(ωt)

Here, the resistance of the resistor is R.

Substitute RImaxsin(ωt) for VR(t), XCImaxsin(ωt+π2) for VC(t), XLImaxsin(ωt+π2) for VL(t) and εmaxsin(ωt+ϕ) for ε(t) in equation (I)

    εmaxsin(ωt+ϕ)=XLImaxsin(ωt+π2)+RImaxsin(ωt)+XCImaxsin(ωt+π2)        (II)

Now, substitute 0 for t in equation (II)

    εmaxsin(ω×0+ϕ)=(XLImaxsin(ω×0+π2)+RImaxsin(ω×0)XCImaxsin(ω×0+π2))εmaxsin(ϕ)=XLImaxsin(π2)+RImaxsin(0)XCImaxsin(π2)εmaxsin(ϕ)=(XLXC)Imax                         (III)

Substitute 2Irms for Imax and 2εrms for εmax in the equation (III).

    2εrmssinϕ=2Irms(XLXC)Irms×2(XLXC)=εrmssinϕIrms                (IV)

Write the expression to calculate the phase angle.

    tanϕ=(XLXCR)                        (V)

Conclusion:

Substitute 23.5° for ϕ, 110V for εrms and 12A for Irms in equation (IV) to calculate the value of (XLXC)

    (XLXC)=110Vsin(23.5°)12A=3.66Ω

Substitute (23.5°) for ϕ and 3.66Ω for XLXC in equation (V) to calculate the value of R.

    tan(23.5°)=(3.66ΩR)R=3.66Ω0.4348=8.41Ω

Therefore, the total resistance in the circuit is 8.41Ω.

(b)

To determine

The net reactance (XLXC).

(b)

Expert Solution
Check Mark

Answer to Problem 59PQ

The net reactance (XLXC) is 3.66Ω.

Explanation of Solution

Conclusion:

Substitute 23.5° for ϕ, 110V for εrms and 12A for Irms in equation (IV) to calculate the value of (XLXC)

    (XLXC)=110Vsin(23.5°)12A=3.66Ω

Therefore, the net reactance (XLXC) is 3.66Ω.

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Chapter 33 Solutions

Physics for Scientists and Engineers: Foundations and Connections

Ch. 33 - Prob. 4PQCh. 33 - Prob. 5PQCh. 33 - Prob. 6PQCh. 33 - Prob. 7PQCh. 33 - Prob. 8PQCh. 33 - Prob. 9PQCh. 33 - Prob. 10PQCh. 33 - Prob. 11PQCh. 33 - At one instant, a current of 6.0 A flows through...Ch. 33 - Prob. 13PQCh. 33 - Prob. 14PQCh. 33 - Prob. 15PQCh. 33 - In Figure 33.9A (page 1052), the switch is closed...Ch. 33 - Prob. 17PQCh. 33 - Prob. 18PQCh. 33 - Prob. 19PQCh. 33 - Prob. 20PQCh. 33 - Prob. 21PQCh. 33 - Prob. 22PQCh. 33 - In the LC circuit in Figure 33.11, the inductance...Ch. 33 - A 2.0-F capacitor is charged to a potential...Ch. 33 - Prob. 26PQCh. 33 - Prob. 27PQCh. 33 - Prob. 28PQCh. 33 - For an LC circuit, show that the total energy...Ch. 33 - Prob. 30PQCh. 33 - Prob. 31PQCh. 33 - Prob. 32PQCh. 33 - Prob. 33PQCh. 33 - Suppose you connect a small lightbulb across a DC...Ch. 33 - Prob. 35PQCh. 33 - Prob. 36PQCh. 33 - Prob. 37PQCh. 33 - Prob. 38PQCh. 33 - Prob. 39PQCh. 33 - Prob. 40PQCh. 33 - Prob. 41PQCh. 33 - Prob. 42PQCh. 33 - Prob. 43PQCh. 33 - In an ideal AC circuit with capacitance, there is...Ch. 33 - Prob. 45PQCh. 33 - Prob. 46PQCh. 33 - Prob. 47PQCh. 33 - Prob. 48PQCh. 33 - Prob. 49PQCh. 33 - An AC generator with an rms emf of 15.0 V is...Ch. 33 - Prob. 51PQCh. 33 - Prob. 52PQCh. 33 - Prob. 53PQCh. 33 - Prob. 54PQCh. 33 - Prob. 55PQCh. 33 - Prob. 56PQCh. 33 - Prob. 57PQCh. 33 - Prob. 58PQCh. 33 - Prob. 59PQCh. 33 - An AC source of angular frequency is connected to...Ch. 33 - An RLC series circuit is constructed with R =...Ch. 33 - Prob. 62PQCh. 33 - A series RLC circuit driven by a source with an...Ch. 33 - Prob. 64PQCh. 33 - Prob. 65PQCh. 33 - Prob. 66PQCh. 33 - Prob. 67PQCh. 33 - Prob. 68PQCh. 33 - Prob. 69PQCh. 33 - Prob. 70PQCh. 33 - Problems 71 and 72 paired. Figure P33.71 shows a...Ch. 33 - Prob. 72PQCh. 33 - Prob. 73PQCh. 33 - Prob. 74PQCh. 33 - Prob. 75PQCh. 33 - In a series RLC circuit with a maximum current of...Ch. 33 - Prob. 77PQCh. 33 - Two coaxial cables of length with radii a and b...Ch. 33 - Prob. 79PQCh. 33 - Prob. 80PQCh. 33 - Prob. 81PQCh. 33 - Prob. 82PQCh. 33 - Prob. 83PQCh. 33 - Prob. 84PQ
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