23.12 RLC Series AC Circuits

An RL circuit consists of a $40.0 Ω$ resistor and a 3.00 mH inductor. (a) Find its impedance $Z$ at 60.0 Hz and 10.0 kHz. (b) Compare these values of $Z$ with those found in the example in which there was also a capacitor.

An LC circuit consists of a $3 . \text{00} \text{mH}$ inductor and a $5 . \text{00} μF$ capacitor. (a) Find its impedance at 60.0 Hz and 10.0 kHz. (b) Compare these values of $Z$ with those found in the example in which there was also a resistor.

To receive AM radio, you want an RLC circuit that can be made to resonate at any frequency between 500 and 1650 kHz. This is accomplished with a fixed $\text{1}.\text{00 }\mu\text{H}$ inductor connected to a variable capacitor. What range of capacitance is needed?

What capacitance do you need to produce a resonant frequency of 1.00 GHz, when using an 8.00 nH inductor?

The lowest frequency in the FM radio band is 88.0 MHz. (a) What inductance is needed to produce this resonant frequency if it is connected to a 2.50 pF capacitor? (b) The capacitor is variable, to allow the resonant frequency to be adjusted to as high as 108 MHz. What must the capacitance be at this frequency?

An RLC series circuit has a $1.00 kΩ$ resistor, a $150 μH$ inductor, and a 25.0 nF capacitor. (a) Find the circuit’s impedance at 500 Hz. (b) Find the circuit’s impedance at 7.50 kHz. (c) If the voltage source has $V_{\text{rms}} = \text{408} \text{V}$, what is $I_{\text{rms}}$ at each frequency? (d) What is the resonant frequency of the circuit? (e) What is $I_{\text{rms}}$ at resonance?

An RLC series circuit has a $1.00 kΩ$ resistor, a $150 μH$ inductor, and a 25.0 nF capacitor. (a) Find the power factor at $f = 7.50 Hz$. (b) What is the phase angle at this frequency? (c) What is the average power at this frequency? (d) Find the average power at the circuit’s resonant frequency.

Referring to the example, find the average power at 10.0 kHz.

A length of 4.000 m of wire is to be used to detect a magnetic field. The wire is made into a single square loop and rotated at a rate of 400 cycles per second. (a) If the magnetic field is 0.02000 T, what is the magnitude of the average emf that can be generated in the first quarter cycle, provided the loop is initially oriented in a plane perpendicular to the magnetic field? (b) Is there a diff…