The impedance of an L-R-C parallel circuit was derived in Problem 31.54. (a) Show that at the resonance angular frequency ω 0 = 1/ L C , the impedance Z is a maximum and therefore the current through the ac source is a minimum, (b) A 100-Ω resistor, a 0.100- μ F capacitor, and a 0.300-H inductor are connected in parallel to a voltage source with amplitude 240 V. What is the resonance angular frequency? For this circuit, what is (c) the maximum current through the source at the resonance frequency; (d) the maximum current in the resistor at resonance; (e) the maximum current in the inductor at resonance; (f) the maximum current in the branch containing the capacitor at resonance?
The impedance of an L-R-C parallel circuit was derived in Problem 31.54. (a) Show that at the resonance angular frequency ω 0 = 1/ L C , the impedance Z is a maximum and therefore the current through the ac source is a minimum, (b) A 100-Ω resistor, a 0.100- μ F capacitor, and a 0.300-H inductor are connected in parallel to a voltage source with amplitude 240 V. What is the resonance angular frequency? For this circuit, what is (c) the maximum current through the source at the resonance frequency; (d) the maximum current in the resistor at resonance; (e) the maximum current in the inductor at resonance; (f) the maximum current in the branch containing the capacitor at resonance?
The impedance of an L-R-C parallel circuit was derived in Problem 31.54. (a) Show that at the resonance angular frequency ω0=
1/
L
C
, the impedance Z is a maximum and therefore the current through the ac source is a minimum, (b) A 100-Ω resistor, a 0.100-μF capacitor, and a 0.300-H inductor are connected in parallel to a voltage source with amplitude 240 V. What is the resonance angular frequency? For this circuit, what is (c) the maximum current through the source at the resonance frequency; (d) the maximum current in the resistor at resonance; (e) the maximum current in the inductor at resonance; (f) the maximum current in the branch containing the capacitor at resonance?
Suppose a 0.55 mH inductor is connected to a 37.5 μF capacitor.
Find the resonant frequency, in hertz.
The simple AC circuit shown on the right has resistance R = 47.5 Ω and impedance Z = 165 Ω. The rms voltage of the power supply is ΔVrms = 196 V.
(a) Express the rms current, Irms, in terms of ΔVrms and Z.
(b) Calculate the numerical value of Irms in amps. (c) Express the average power dissipated in the circuit, Pavg, in terms of Irms and R. (d) Calculate the value of Pavg, in watts.
An L-R-C series circuit consists of a 2.70 μF capacitor, a 5.00 mH inductor, and a 50.0 Ω resistor connected across an ac source of voltage amplitude 14.0 V having variable frequency.
A. Under the conditions of part A (ω = 2.09×104 rad/s), what is the average power delivered to each circuit element? (PR,PC,PL)
B. What is the maximum current through the capacitor?
In an L-R-C series circuit, suppose R = 300 ohms, L = 60 mH, C = 0.50 uF, V = 50 V, and w = 10,000 rad/s. Find the 1) reactances XL and XC, 2) the impedance Z, 3) the current amplitude I, 4) the phase angle φ, and 5) the voltage amplitude across each circuit element (inductor, resistor, capacitor).
Chapter 31 Solutions
University Physics with Modern Physics (14th Edition)
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