For the series circuit of Fig. 20.50: a. Find the value of X1 for resonance. b. Determine the magnitude of the current I at reso- + VR R = 20 nance. + c. Find the voltages VR, VL and Vc at resonance, and compare their magnitudes. d. Determine the quality factor of the circuit. Is it a high- or low-Q circuit? e. If the resonant frequency is 5 kHz, determine the value of L and C. E () 20 mV Xc 40 Ω Vε FIG. 20.50 f. Find the bandwidth of the response if the resonant fre- quency is 5 kHz. g. What are the low and high cutoff frequencies? Problem 3.

An RLC series circuit hag a 1.00 k(register, a 150 (H 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) It the voltage source has Vrms = 408 V, what is Irms at each frequency? (d) What is the resonant frequency of the circuit? (e) What is Irms at resonance?

In an RLC series circuit, the voltage amplitude and frequency of the source are 100 V and 500 Hz, respectively, an R = 5O0. L=0.20H, and C=2.0F . (a)What is the impedance of the circuit? (b) What is the amplitude of the current from the source? (C) If the emf of the source Is given by v(tt)=(100V)sin , how does the current vary with time? (d) Repeat the calculations with C changed to 0.20F .

What is the self-inductance of an LC circuit that oscillates at 60 Hz 1ien the capacitance is 10 F ?

A step-up transformer is designed so that the output of its secondary winding is 2000 V(rms) when the primary winding is connected to a 110-V (rms) line voltage, (a) If there are 100 turns in the primary winding, how many turns are there in the secondary winding? (b) If a resistor connected across the secondary winding draws an rms current of 0.75 A. what is the current in die primary winding?

An RLC series circuit has a 2.50 (resistor, a 100 (H inductor, and an 80.0 (F capacitor. (a) Find the circuit's impedance at 120 Hz. (b) Find the circuit’s impedance at 5.00 kHz. (c) If the voltage source has Vrms = 5.60 V, what is Irms at each frequency? (d) What is the resonant frequency of the circuit? (e) What is Irms at resonance?

Check Your Understanding In the circuit of Figure 15.11, L=2.0103H,C=5.0104F , and R=40 (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 depends on the values of R, C, and L.

What is the plia.se angle in a series RLC circuit at resonance? (a) 180 (b) 90 (c) 0 (d) 90 (e) None of those answers is necessarily correct.

Calculate the reactance of a 5.0F capacitor at (a) 60 Hz, (b) 600 Hz, and (c) 6000 Hz.

The RC high-pass filter shown in Figure P33.53 has a resistance R = 0.500 and a capacitance C = 613 F. What is the ratio of the amplitude of the output voltage to that of the input voltage for this filter for a source frequency of 600 Hz?