Check Your Understanding In the circuit of Figure 15.11, L = 2.0 × 10 − 3 H, C =5 .0 × 10 − 4 F , and R = 40 Ω (a) What is the resonant frequency? (b) What Is the Impedance of the circuit at resonance? (c) If the voltage amplitude is 10 V, what is i ( t ) at resonance? (d) The frequency of the AC generator is now changed to 200 Hz. Calculate the phase difference between the current and the emf of the generator. The ac circuit shown in Figure 15.11, called an RLC series circuit, is a series combination of a resistor, capacitor, and inductor connected across an ac source. It produces an emf of Figure 15.11 (a) An RLC series circuit, (b) A comparison of the generator output voltage and the current the value of the phase difference ϕ depends on the values of R , C , and L.
Check Your Understanding In the circuit of Figure 15.11, L = 2.0 × 10 − 3 H, C =5 .0 × 10 − 4 F , and R = 40 Ω (a) What is the resonant frequency? (b) What Is the Impedance of the circuit at resonance? (c) If the voltage amplitude is 10 V, what is i ( t ) at resonance? (d) The frequency of the AC generator is now changed to 200 Hz. Calculate the phase difference between the current and the emf of the generator. The ac circuit shown in Figure 15.11, called an RLC series circuit, is a series combination of a resistor, capacitor, and inductor connected across an ac source. It produces an emf of Figure 15.11 (a) An RLC series circuit, (b) A comparison of the generator output voltage and the current the value of the phase difference ϕ depends on the values of R , C , and L.
Check Your Understanding In the circuit of Figure 15.11,
L
=
2.0
×
10
−
3
H,
C
=5
.0
×
10
−
4
F
, and
R
=
40
Ω
(a) What is the resonant frequency? (b) What Is the Impedance of the circuit at resonance? (c) If the voltage amplitude is 10 V, what is
i
(
t
)
at resonance? (d) The frequency of the AC generator is now changed to 200 Hz. Calculate the phase difference between the current and the emf of the generator. The ac circuit shown in Figure 15.11, called an RLC series circuit, is a series combination of a resistor, capacitor, and inductor connected across an ac source. It produces an emf of Figure 15.11 (a) An RLC series circuit, (b) A comparison of the generator output voltage and the current the value of the phase difference
ϕ
depends on the values of R, C, and L.
In the AC circuit as shown, R = 70.0 Ω and the output voltage of the AC source is ΔVmax sin ωt. (a) If ΔVR = 0.250 ΔVmax for the first time at t = 0.010 0 s, what is the angular frequency of the source? (b) What is the next value of t for which ΔVR = 0.250 ΔVmax?
You have a 200 Ω resistor, a 0.400 H inductor, a 5.00 µF capacitor, and a variable-frequency ac source with an amplitude of 3.00 V. You connect all four elements together to form a series circuit. (a) At what frequency will the current in the circuit be greatest? What will be the current amplitude at this frequency? (b) What will be the current amplitude at an angular frequency of 400 rad/s? At this frequency, will the source voltage lead or lag the current?
A resistor and capacitor are connected in series acrossan ac generator. The emf of the generator is given byv(t) = V0cos ωt, where V0 = 120 V,ω = 120π rad/s, R = 400 Ω, and C = 4.0µF. (a) Whatis the impedance of the circuit? (b) What is the amplitudeof the current through the resistor? (c) Write an expressionfor the current through the resistor. (d) Write expressionsrepresenting the voltages across the resistor and across thecapacitor.
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