Figure 31-24 shows three situations like those in Fig. 31-15. Is the driving angular frequency greater than, less than, or equal to the resonant angular frequency of the circuit in (a) situation 1, (b) situation 2, and (c)situation 3?
Figure 31-24 shows three situations of frequencies.
When the current leads the emf, then the angular frequency is less and vice versa. This case of current leading indicates flowing through a capacitor. If current lags the emf, this is when the current flows through an inductor.
The current I leads the driving emf E, so angular frequency is less than the resonant frequency.
The current I and the driving emf E have the same phase difference, so angular frequency is equal to the resonant frequency.
The current I is larger than the driving emf E, so the angular frequency is greater than the resonant frequency.
Remove the capacitor from the circuit in Figure and set , and . (a)What is the Z? (b)What is the ? (c)What is the I? (d) Draw a phasor diagram.
Fig: A single-loop circuit containing a resistor, a capacitor, and an inductor. A generator, represented by a sine wave in a circle, produces an alternating emf that establishes an alternating current; the directions of the emf and current are indicated here at only one instant.
An alternating source with a variable frequency, a capacitor with capacitance C, and a resistor with resistance R are connected in series. Figure gives the impedance Z of the circuit versus the driving angular frequency ; the curve reaches an asymptote of , and the horizontal scale is set by . The figure also gives the reactance for the capacitor versus . What are (a) What is R ?(b) What is C ?
An ac generator provides emf to a resistive load in a remote factory over a two-cable transmission line. At the factory a stepdown transformer reduces the voltage from its (rms) transmission value to a much lower value that is safe and convenient for use in the factory. The transmission line resistance is , and the power of the generator is . If , what are (a) the voltage decreases V along the transmission line and (b) the rate at which energy is dissipated in the line as thermal energy? If , what are (c) V and (d) ? If , what are (e) V and (f) ?
Consider the circuit shown in Fig. 31-40. With the switch S1 closed and the other two switches open, the circuit has a time constant . With the switch S2 closed and the other two switches open, the circuit has a time constant . With the switch S3 closed and the other two switches open, the circuit oscillates with a period T. Show that
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