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Chapter 31: Q82P (page 940)

A 1.50mHinductor in an oscillatingLCcircuit stores a maxi- mum energy of 10.0μJ. What is the maximum current?

Short Answer

Expert verified

The maximum current is0.115A.

Step by step solution

01

Step 1: Given

Umax=100μJ=10×10-6J

L=1.5mH=1.5×10-3H

02

Determining the concept

By using the formula for maximum energy in the LCcircuit and substituting the given values, find the maximum current.

Formulae are as follows:

Umax=12LI2

Where,

U = magnetic energy.

L = inductance of solenoid.

I = current.

03

Determining the maximum current

Umax=12LI2

Rearranging the terms,

I2=2UmaxLI=2UmaxLI=2×10×10-61.5×10-3I=0.005A

Hence,the maximum current is0.005A.

Using the formula for maximum energy stored in the LC circuit, found the maximum current in the circuit.

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Most popular questions from this chapter

In Fig. 31-38, a three-phase generator G produces electrical power that is transmitted by means of three wires. The electric potentials (each relative to a common reference level) are V1=Asinωdtfor wire 1, V2=Asin(ωdt-1200) for wire 2, and V3=Asin(ωdt-2400)for wire 3. Some types of industrial equipment (for example, motors) have three terminals and are designed to be connected directly to these three wires. To use a more conventional two-terminal device (for example, a lightbulb), one connects it to any two of the three wires. Show that the potential difference between any two of the wires (a) oscillates sinusoidally with angular frequency ωdand (b) has an amplitude ofA3.

In an oscillating LCcircuit withL=50mHandC=40μF, the current is initially a maximum. How long will it take before the capacitor is fully charged for the first time?

In an RLC circuit such as that of Fig. 31-7 assume that R=5.0Ω,L=60.0mH,fd=60.0Hzand εm=30.0V. For what values of the capacitance would the average rate at which energy is dissipated in the resistance be (a) a maximum and (b) a minimum? What are (c) the maximum dissipation rate and the corresponding (d) phase angle and (e) power factor? What are (f) the minimum dissipation rate and the corresponding (g) phase angle and (h) power factor?

A 0.50kgbody oscillates in SHM on a spring that, when extended2.0mmfrom its equilibrium position, has a8.0Nrestoring force. (a) What is the angular frequency of oscillation?(b) What is the period of oscillation (c) What is the capacitance of an LCcircuit with the same period if Lis5.0H?

An ac generator with emf amplitude εm=220V and operating at frequency fd=400Hzcauses oscillations in a seriesRLC circuit having R=220Ω,L=150mH , andC=24.0μF . Find (a) the capacitive reactance XC, (b) the impedance Z, and (c) the current amplitude I. A second capacitor of the same capacitance is then connected in series with the other components. Determine whether the values of (d)XC , (e) Z, and (f) Iincrease, decrease, or remain the same.

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