(II) The frequency of the ac voltage source (peak voltage V 0 ) in an LRC circuit is tuned to the circuit’s resonant frequency, f 0 = 1 / ( 2 π L C ) , ( a ) Show that the peak voltage across the capacitor is V C 0 ·= V 0 T 0 /2 π τ), where T 0 (= 1/ f 0 ) is the period of the resonant frequency and τ = RC is the time constant for charging the capacitor C through a resistor R . ( b ) Define β = T 0 /(2 πτ ) so that V C 0 = βV 0 . Then β is the “amplification” of the source voltage across the capacitor. If a particular LRC circuit contains a 2.0-nF capacitor and has a resonant frequency of 5.0 kHz, what value of R will yield β = 125?
(II) The frequency of the ac voltage source (peak voltage V 0 ) in an LRC circuit is tuned to the circuit’s resonant frequency, f 0 = 1 / ( 2 π L C ) , ( a ) Show that the peak voltage across the capacitor is V C 0 ·= V 0 T 0 /2 π τ), where T 0 (= 1/ f 0 ) is the period of the resonant frequency and τ = RC is the time constant for charging the capacitor C through a resistor R . ( b ) Define β = T 0 /(2 πτ ) so that V C 0 = βV 0 . Then β is the “amplification” of the source voltage across the capacitor. If a particular LRC circuit contains a 2.0-nF capacitor and has a resonant frequency of 5.0 kHz, what value of R will yield β = 125?
(II) The frequency of the ac voltage source (peak voltage V0) in an LRC circuit is tuned to the circuit’s resonant frequency,
f
0
=
1
/
(
2
π
L
C
)
, (a) Show that the peak voltage across the capacitor is VC0·= V0T0/2π τ), where T0(= 1/f0) is the period of the resonant frequency and τ = RC is the time constant for charging the capacitor C through a resistor R. (b) Define β = T0/(2πτ) so that VC0 = βV0. Then β is the “amplification” of the source voltage across the capacitor. If a particular LRC circuit contains a 2.0-nF capacitor and has a resonant frequency of 5.0 kHz, what value of R will yield β = 125?
(b) An AC voltage source of V = 310 sin (25?t) is connected to a 140 Ω resistor, where V is in Volts and t is in seconds. Calculate the rms current across the resistor.
(III) (a) What is the rms current in an LR circuit when a60.0-Hz 120-V rms ac voltage is applied, where R=2.80kΩand L= 3.50mH? (b) What is the phase angle betweenvoltage and current? (c) How much power is dissipated?(d) What are the rms voltage readings across R and L?
(II) For a 120-V rms 60-Hz voltage, an rms current of 70 mApassing through the human body for 1.0 s could be lethal.What must be the impedance of the body for this to occur?
Chapter 30 Solutions
Physics for Scientists and Engineers with Modern Physics
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