(a) Explanation Write the expression for the self-inductance. L = N Φ B I (I) Here, L is the self-inductance, N is the number of turns, Φ B is the flux, I is the current. Write the expression for the Φ B . Φ B = B A (II) Here, B is the magnetic field, A is the area of the loop. Write the expression for the B . B = μ 0 N I 2 π r 0 (III) Here, r 0 is the radius of the toroid, μ 0 is the permeability of free space. Write the expression for A . A = π d 2 4 (IV) Here, d is the diameter of the loop. Use equation (IV), (III) in (II) to solve for Φ B (b) To determine The self-inductance of the large toroid.

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Chapter 30, Problem 74GP

(a)

To determine

Show that the self-inductance L≈μ0N2d28r0

(b)

To determine

The self-inductance of the large toroid.

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Chapter 30, Problem 73GP

Chapter 30, Problem 75GP

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Chapter 30 Solutions

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Ch. 30.1 - Prob. 1AE Ch. 30.1 - Prob. 1BE Ch. 30.3 - Prob. 1CE Ch. 30.4 - Show that L/R does have dimensions of lime. (See...Ch. 30.4 - Prob. 1EE Ch. 30.5 - Return to the Chapter-Opening Question, page 785,...Ch. 30.7 - At what frequency is the reactance of a 1.0-F...Ch. 30.7 - Prob. 1HE Ch. 30 - Prob. 1Q Ch. 30 - Prob. 2Q

Ch. 30 - Prob. 3Q Ch. 30 - Prob. 4Q Ch. 30 - If you are given a fixed length of wire, how would...Ch. 30 - Prob. 6Q Ch. 30 - Prob. 7Q Ch. 30 - Prob. 8Q Ch. 30 - What keeps an LC circuit oscillating even after...Ch. 30 - Is the ac current in the indicator always the same...Ch. 30 - Prob. 11Q Ch. 30 - In an ac LRC circuit, if XL XC, the circuit is...Ch. 30 - Prob. 13Q Ch. 30 - Under what conditions is the impedance in an LRC...Ch. 30 - Is it possible for the instantaneous power output...Ch. 30 - In an ac LRC circuit, does the power factor, cos,...Ch. 30 - Describe briefly how the frequency of the source...Ch. 30 - Prob. 18Q Ch. 30 - In an LRC circuit, the current and the voltage in...Ch. 30 - Compare the oscillations or an LRC circuit to the...Ch. 30 - Prob. 1P Ch. 30 - Prob. 2P Ch. 30 - Prob. 3P Ch. 30 - Prob. 4P Ch. 30 - (I) If the current in a 280-mH coil changes...Ch. 30 - Prob. 6P Ch. 30 - Prob. 7P Ch. 30 - Prob. 8P Ch. 30 - Prob. 9P Ch. 30 - (II) If the outer conductor of a coaxial cable has...Ch. 30 - Prob. 11P Ch. 30 - Prob. 12P Ch. 30 - Prob. 13P Ch. 30 - (II) Ignoring any mutual inductance, what is the...Ch. 30 - (I) The magnetic field inside an air-filled...Ch. 30 - (I) Typical large values for electric and magnetic...Ch. 30 - (II) What is the energy density at the center of a...Ch. 30 - (II) Calculate the magnetic and electric energy...Ch. 30 - Prob. 19P Ch. 30 - (II) Determine the total energy stored per unit...Ch. 30 - (II) Determine the total energy stored per unit...Ch. 30 - Prob. 22P Ch. 30 - (II) How many time constants does it take for the...Ch. 30 - (II) It takes 2.56 ms for the current in an LR...Ch. 30 - Prob. 25P Ch. 30 - (II) In the circuit of Fig. 3027, determine the...Ch. 30 - Prob. 27P Ch. 30 - Prob. 28P Ch. 30 - (II) A 12-V battery has been connected to an LR...Ch. 30 - Prob. 30P Ch. 30 - (I) The variable capacitor in the tuner of an AM...Ch. 30 - Prob. 32P Ch. 30 - (II) In some experiments, short distances are...Ch. 30 - Prob. 34P Ch. 30 - Prob. 35P Ch. 30 - Prob. 36P Ch. 30 - Prob. 37P Ch. 30 - Prob. 38P Ch. 30 - (I) At what frequency will a 32.0-mH inductor have...Ch. 30 - (I) What is the reactance of a 9.2-F capacitor at...Ch. 30 - (I) Plot a graph of the reactance of a 1.0-F...Ch. 30 - (I) Calculate the reactance of, and rms current...Ch. 30 - (II) A resistor R is in parallel with a capacitor...Ch. 30 - Prob. 44P Ch. 30 - (II) (a) What is the reactance of a 0.086-F...Ch. 30 - Prob. 46P Ch. 30 - (II) A current I = 1.80 cos 377t (I in amps, t in...Ch. 30 - (I) A 10.0-k resistor is in series with a 26.0-mH...Ch. 30 - (I) A 75- resistor and a 6.8-F capacitor are...Ch. 30 - (I) For a 120-V, 60-Hz voltage, a current of 70 mA...Ch. 30 - (II) A 2.5-k resistor in series with a 420-mH...Ch. 30 - (II) (a) What is the rms current in a series RC...Ch. 30 - (II) An ac voltage source is connected in series...Ch. 30 - (II) Determine the total impedance, phase angle,...Ch. 30 - (II) (a) What is the rms current in a series LR...Ch. 30 - (II) A 35-mH inductor with 2.0- resistance is...Ch. 30 - (II) A 25-mH coil whose resistance is 0.80 is...Ch. 30 - (II) A 75-W lightbulb is designed to operate with...Ch. 30 - (II) In the LRC circuit or Fig. 3019, suppose I =...Ch. 30 - (II) An LRC series circuit with R = 150 , L = 25...Ch. 30 - (II) An LR circuit can be used as a phase shifter....Ch. 30 - (I) A 3800-pF capacitor is connected in series to...Ch. 30 - (I) What is the resonant frequency of the LRC...Ch. 30 - (II) An LRC circuit has L = 4.15 mH and R = 3.80...Ch. 30 - (II) The frequency of the ac voltage source (peak...Ch. 30 - (II) Capacitors made from piezoelectric materials...Ch. 30 - (II) (a) Determine a formula for the average power...Ch. 30 - (II) (a) Show that oscillation of charge Q on the...Ch. 30 - (II) A resonant circuit using a 220-nF capacitor...Ch. 30 - Prob. 70P Ch. 30 - Prob. 71GP Ch. 30 - Prob. 72GP Ch. 30 - At time t = 0, the switch in the circuit shown in...Ch. 30 - Prob. 74GP Ch. 30 - Prob. 75GP Ch. 30 - Assuming the Earths magnetic field averages about...Ch. 30 - (a) For an underdamped LRC circuit, determine a...Ch. 30 - An electronic device needs to be protected against...Ch. 30 - Prob. 79GP Ch. 30 - Prob. 80GP Ch. 30 - An ac voltage source V=V0sin(t+90) is connected...Ch. 30 - A circuit contains two elements, but it is not...Ch. 30 - A 3.5-k resistor in series with a 440-mH inductor...Ch. 30 - (a) What is the rms current in on RC circuit if R...Ch. 30 - An inductance coil draws 2.5 A de when connected...Ch. 30 - The Q-value of a resonance circuit can be defined...Ch. 30 - Show that the fraction of electromagnetic energy...Ch. 30 - In a series LRC circuit, the inductance is 33mH,...Ch. 30 - Prob. 89GP Ch. 30 - A voltage V = 0.95 sin 754t is applied to an LRC...Ch. 30 - Filler circuit. 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Show that the self-inductance L ≈ μ 0 N 2 d 2 8 r 0

Solution Summary: The author analyzes the self-inductance of Lapprox mu, NPhi, and BI.

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Show that the self-inductance L≈μ0N2d28r0

The self-inductance of the large toroid.

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Chapter 30 Solutions