Explanation Given data: R is 24 Ω . L is 58 μ H . f 0 is 320 kHz Formula used: Consider the expression for peak current at any frequency ( I ) . I = ε 0 R 2 + ( X L − X C ) 2 (1) Here, ε 0 is the initial voltage, R is the resistance, X L is the inductive reactance, and X C is the capacitive reactance. Consider the expression for resonance frequency ( f 0 ) . f 0 = 1 2 π L C (2) Here, C is the capacitance, and L is the inductance. Consider the expression for capacitive reactance ( X C ) . X C = 1 2 π f C Here, f is the frequency. Consider the expression for inductive reactance ( X L ) . X L = 2 π f L Explanation: Rearrange equation (2) to find capacitance. C = ( 1 2 π f 0 ) 2 L Substitute 320 kHz for f 0 and 58 μ H for L , C = [ 1 2 π ( 320 kHz ) ] 2 58 μ H = [ 1 2 π ( 320 × 10 3 Hz ) ] 2 58 × 10 − 6 H = ( 1 2.010 × 10 6 Hz ) 2 58 × 10 − 6 H = 2.475 × 10 − 13 58 × 10 − 6 F C = 4.267 × 10 − 9 F At resonance condition, the inductive reactance is equal to the capacitive reactance ( X L = X C ) . Modify equation (1) as follows. I = ε 0 R 2 + ( X L − X C ) 2 = ε 0 R 2 = ε 0 R Since the current in the circuit is one-half its value at resonance, then modify the equation as follows. I = ε 0 2 R Substitute ε 0 2 R for I in equation (1), ε 0 2 R = ε 0 R 2 + ( X L − X C ) 2 1 2 R = 1 R 2 + ( X L − X C ) 2 R 2 + ( X L − X C ) 2 = 2 R X L − X C = ( 2 R ) 2 − R 2 Simplify the equation

Pearson eText for College Physics: A Strategic Approach -- Instant Access (Pearson+)

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ISBN: 9780137561520

Author: Randall Knight, Brian Jones

Publisher: PEARSON+

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Chapter 26, Problem 54P

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The value of frequency.

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Chapter 26, Problem 53P

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Chapter 26 Solutions

Pearson eText for College Physics: A Strategic Approach -- Instant Access (Pearson+)

Ch. 26 - Identical resistors are connected to separate 12 V...Ch. 26 - Prob. 2CQ Ch. 26 - Most battery-powered devices wont work if you put...Ch. 26 - Prob. 4CQ Ch. 26 - A soldering gun contains a transformer that lowers...Ch. 26 - A 12 V DC power supply is connected to the primary...Ch. 26 - Figure Q26.7 shows three wires wrapped around an...Ch. 26 - Women usually have higher resistance of their arms...Ch. 26 - If you work out enough to visibly increase the...Ch. 26 - Prob. 10CQ

Ch. 26 - Prob. 11CQ Ch. 26 - Prob. 12CQ Ch. 26 - The peak current through a capacitor is 2.0 A....Ch. 26 - Prob. 14CQ Ch. 26 - Prob. 16CQ Ch. 26 - Figure Q26.17 shows two inductors and the...Ch. 26 - The peak current passing through an inductor is...Ch. 26 - Consider the four circuits in Figure Q26.19. Rank...Ch. 26 - Prob. 20CQ Ch. 26 - The resonance frequency of a driven RLC circuit is...Ch. 26 - Consider the four circuits in Figure Q26.22. They...Ch. 26 - Prob. 23MCQ Ch. 26 - An inductor is connected to an AC generator. As...Ch. 26 - A capacitor is connected to an AC generator. As...Ch. 26 - An AC source is connected to a series combination...Ch. 26 - An AC source is connected to a series combination...Ch. 26 - The circuit shown in Figure Q26.28 has a resonance...Ch. 26 - At resonance, a driven RLC circuit has VC = 5.0 V,...Ch. 26 - A driven RLC circuit has VC = 5.0V, VR = 7.0 V,...Ch. 26 - A 200 resistor is connected to an AC source with...Ch. 26 - Figure P26.2 shows voltage and current graphs for...Ch. 26 - A resistor dissipates 2.00 W when the rms voltage...Ch. 26 - The heating element of a hair dryer dissipates...Ch. 26 - A toaster oven is rated at 1600 W for operation at...Ch. 26 - Prob. 6P Ch. 26 - A generator produces 40 MW of power and sends it...Ch. 26 - Soles of hoots that are designed to protect...Ch. 26 - The primary coil of a transformer is connected to...Ch. 26 - Prob. 10P Ch. 26 - A power pack charging a cell phone battery has an...Ch. 26 - A neon sign transformer has a 450 W AC output with...Ch. 26 - Prob. 13P Ch. 26 - Prob. 14P Ch. 26 - A generator produces 250 kW of electric power at...Ch. 26 - In an old house, the wires leading lo a 120 V...Ch. 26 - A typical American family uses 1000 kWh of...Ch. 26 - Prob. 18P Ch. 26 - The following appliances are connected to a single...Ch. 26 - Prob. 20P Ch. 26 - A 60 W (120 V) night light is turned on for an...Ch. 26 - Prob. 22P Ch. 26 - The manufacturer of an electric table saw claims...Ch. 26 - John is changing a lightbulb in a lamp, Its a warm...Ch. 26 - In some countries AC outlets near bathtubs are...Ch. 26 - If you touch the terminal of a battery, the small...Ch. 26 - A person standing barefoot on the ground 20 m from...Ch. 26 - A fisherman has netted a torpedo ray. As he picks...Ch. 26 - Problems 30 and 31 concern a high-voltage...Ch. 26 - Problems 30 and 31 concern a high-voltage...Ch. 26 - A 0.30 F capacitor is connected across an AC...Ch. 26 - A 20 F capacitor is connected across an AC...Ch. 26 - The peak current through a capacitor is 10.0 mA....Ch. 26 - Prob. 35P Ch. 26 - Prob. 36P Ch. 26 - The peak current through a capacitor is 8.0 mA...Ch. 26 - Prob. 38P Ch. 26 - A 20 mH inductor is connected across an AC...Ch. 26 - Prob. 40P Ch. 26 - A 500 H inductor is connected across an AC...Ch. 26 - An inductor is connected to a 15 kHz oscillator...Ch. 26 - The peak current through an inductor is 12.5 mA...Ch. 26 - A 2.0 mH inductor is connected in parallel with a...Ch. 26 - An FM radio station broadcasts at a frequency of...Ch. 26 - The inductor in the RLC tuning circuit of an AM...Ch. 26 - At what frequency f do a 1.0 F capacitor and a 1.0...Ch. 26 - What capacitor in series with a 100 resistor and...Ch. 26 - What inductor in series with a 100 resistor and a...Ch. 26 - A series RLC circuit has a 200 kHz resonance...Ch. 26 - An RLC circuit with a 10 F capacitor is connected...Ch. 26 - Prob. 52P Ch. 26 - A series KLC circuit consists of a 280 resistor,...Ch. 26 - Prob. 54P Ch. 26 - Electric outlets in England are 230 V. Alice...Ch. 26 - Prob. 56GP Ch. 26 - Prob. 57GP Ch. 26 - The voltage across a 60 F capacitor is described...Ch. 26 - Prob. 59GP Ch. 26 - An electronics hobbyist is building a radio set to...Ch. 26 - Prob. 61GP Ch. 26 - Prob. 62GP Ch. 26 - An RLC circuit consists of a 48 resistor, a 200 F...Ch. 26 - Cell Membrane Resistance The capacitance of...Ch. 26 - Cell Membrane Resistance The capacitance of...Ch. 26 - Cell Membrane Resistance The capacitance of...Ch. 26 - Cell Membrane Resistance The capacitance of...Ch. 26 - Halogen Bulbs Halogen bulbs have some differences...Ch. 26 - Halogen Bulbs Halogen bulbs have some differences...Ch. 26 - Halogen Bulbs Halogen bulbs have some differences...Ch. 26 - Halogen Bulbs Halogen bulbs have some differences...

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