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Chapter 31: Q12Q (page 935)

Figure 31-25 shows the currentand driving emf 蔚for a series RLC circuit. (a) Does the current lead or lag the emf? (b) Is the circuit鈥檚 load mainly capacitive or mainly inductive? (c) Is the angular frequency 蝇dof the emf greater than or less than the natural angular frequency 蝇?

Short Answer

Expert verified
  1. The current leads the emf.
  2. The circuit鈥檚 load is mainly capacitive.
  3. The angular frequency 蝇dis less than the natural angular frequency.

Step by step solution

01

The given data

Figure 31-25 showing current and driving emf for a series RLC circuit is given.

02

Understanding the concept of current and emf of RLC circuit

We can predict whether the current leads or lags the emf by observing the given figure. From this, we can find the type of circuit鈥檚 load and whether the angular frequency is less than the natural angular frequency. If the current is leading the emf voltage, it is considered to be capacitive and if lagging, it is considered to be inductive.

03

a) Calculation to predict whether the current is leading or lagging

In the given figure, we can observe that the current peaks at an earlier time than the emf.

Therefore, current leads the emf.

04

b) Calculation to predict whether the circuit load

Since current leads the emf, the circuit鈥檚 load is mainly capacitive.

05

c) Calculation to predict whether the angular frequency is less or greater than natural frequency

Since current leads the emf and phase constant is negative, the angular frequency 蝇dis less than the natural angular frequency.

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Most popular questions from this chapter

An alternating emf source with a variable frequency fd is connected in series with a80.0惟resistor and an 40.0mHinductor. The emf amplitude is6.0V. (a) Draw a phasor diagram for phasor VR(the potential across the resistor) and phasor VL(the potential across the inductor). (b) At what driving frequency fddo the two phasors have the same length? At that driving frequency, what are (c) the phase angle in degrees, (d) the angular speed at which the phasors rotate, and (e) the current amplitude?

A variable capacitor with a range from 10 to 365pF is used with a coil to form a variable-frequency LCcircuit to tune the input to a radio. (a) What is the ratio of maximum frequency to minimum frequency that can be obtained with such a capacitor? If this circuit is to obtain frequencies from 0.54 MHz to 1.6 0MHz, the ratio computed in (a) is too large. By adding a capacitor in parallel to the variable capacitor, this range can be adjusted. To obtain the desired frequency range,(b) What capacitance should be added ? (c) What inductance should the coil have?

An alternating source with a variable frequency, a capacitor with capacitance C, and a resistor with resistance Rare connected in series. Figure gives the impedance Zof the circuit versus the driving angular frequency蝇d; the curve reaches an asymptote of 500惟, and the horizontal scale is set by(蝇d)s=300rad/s. The figure also gives the reactance XCfor the capacitor versus蝇d. What are (a) What is R ?(b) What is C?

Using the loop rule, derive the differential equation for an LCcircuit (EquationLd2qdt2+1Cq=0).

In an oscillating series RLC circuit, find the time required for the maximum energy present in the capacitor during an oscillation to fall to half its initial value. Assume q=Qatt=0s
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