A motor attached to a 120 V/60 Hz power line draws an 8.0 A current. Its average energy dissipation is 800 W. How much series capacitance needs to be added to increase the power factor to 1.0?
31. Alternating Current
Series LRC Circuits
- Textbook Question747views
- Textbook Question
A series RLC circuit with ε0 = 10.0 V consists of a 1.0 Ω resistor, a 1.0 μH inductor, and a 1.0 μF capacitor. What is V1 at ω = ω0 and at ω = ω1?
108views - Textbook Question
The tuning circuit in an FM radio receiver is a series RLC circuit with a 0.200 μH inductor. FM radio stations are assigned frequencies every 0.2 MHz, but two nearby stations cannot use adjacent frequencies. What is the maximum resistance the tuning circuit can have if the peak current at a frequency of 103.9 MHz, the closest frequency that can be used by a nearby station, is to be no more than 0.10% of the peak current at 104.3 MHz? The radio is still tuned to 104.3 MHz, and you can assume the two stations have equal strength.
942views - Textbook Question
(a) What is the rms current in a series LR circuit when a 60.0-Hz, 120-V rms ac voltage is applied, where R = 965 Ω and L = 255 mH? (b) What is the phase angle between voltage and current? (c) How much power is dissipated? (d) What are the rms voltage readings across R and L?
826views - Textbook Question
A series RLC circuit consists of a 50 Ω resistor, a 3.3 mH inductor, and a 480 nF capacitor. It is connected to a 5.0 kHz oscillator with a peak voltage of 5.0 V. What is the instantaneous current i when ε = ε0?
79views - Textbook Question
For the circuit of FIGURE EX32.32, Find VR and VL at resonance.
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Show that the fraction of electromagnetic energy lost (to thermal energy) per cycle in a lightly damped (R² ≪ 4L/C) LRC circuit is approximately . The quantity Q can be defined as Q = Lω/R, and is called the Q-value, or quality factor, of the circuit and is a measure of the damping present. A high Q-value means smaller damping and less energy input required to maintain oscillations.
600views - Textbook Question
Suppose a series LRC circuit has two resistors, R₁ and R₂, two capacitors, C₁ and C₂, and two inductors, L₁ and L₂ all in series. Calculate the total impedance of the circuit.
523views - Textbook Question
An inductance coil draws 2.2 A dc when connected to a 45-V battery. When connected to a 60.0-Hz 120-V (rms) source, the current drawn is 3.8 A (rms). Determine the inductance and resistance of the coil.
522views - Textbook Question
An ac voltage source is connected in series with a 2.0-μF capacitor and a 750-Ω resistor. Using a digital ac voltmeter, the voltage source is measured to be 4.0 V rms, and the voltages across the resistor and across the capacitor are found to be 3.0 V rms and 2.7 V rms, respectively. Determine the frequency of the ac voltage source. Why is the voltage measured across the voltage source not equal to the sum of the voltages measured across the resistor and across the capacitor?
587views - Textbook Question
A circuit contains two elements, but it is not known if they are L, R, or C. The current in this circuit when connected to a 120-V rms 60.0-Hz source is 5.6 A and lags the voltage by 55°. What are the two elements and what are their values?
155views - Textbook Question
For an underdamped LRC circuit, determine a formula for the energy U = UE + UB stored in the electric and magnetic fields as a function of time. Give answer in terms of the initial charge Qo on the capacitor.
686views - Textbook Question
For an underdamped LRC circuit, determine a formula for the energy U = UE + UB stored in the electric and magnetic fields as a function of time. Give answer in terms of the initial charge Qo on the capacitor. Show how dU/dt is related to the rate energy is transformed in the resistor, I2R.
565views - Textbook Question
An inductor L in series with a resistor R, driven by a sinusoidal voltage source, responds as described by the following differential equation: Show that a current of the form I = I0 sin (ωt - Φ) flows through the circuit by direct substitution into the differential equation. Determine the amplitude of the current (I0) and the phase difference Φ between the current and the voltage source.
332views - Textbook Question
(II) An LRC series circuit with R = 120 Ω, L = 25 mH, and C = 2.0 μF is powered by an ac voltage source of peak voltage V0 = 340 V and frequency f = 660 Hz. Determine the peak current that flows in this circuit.
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