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A charged capacitor and an inductor are connected at time t=0. In terms of the period T of the resulting oscillations, what is the first later time at which the following reach a maximum: (a)UB, (b) the magnetic flux through the inductor, (c) di/dt
, and (d) the EMF of the inductor?

Short Answer

Expert verified
  1. The value of UBis maximum at T/4.
  2. The magnetic flux through the inductor is maximum atT/4.
  3. The value of di/dtis maximum atT/2.
  4. The EMF of the inductor is maximum at T/2.

Step by step solution

01

The given data

A charged capacitor and an inductor are connected at time t=0.

02

Understanding the concept of the LC circuit mechanism

In an LC circuit, the charging and discharging of the capacitor occurs periodically. The total energy of the circuit remains constant and is distributed as magnetic energy and electrical energy. The proportion of the two types of energies varies periodically.

03

a) Calculation of the time at which the magnetic field energy is maximum

The charged capacitor and the inductor are connected t=0. The charged capacitor starts discharging through the inductor. Thus, the magnetic energy of the inductor goes on increasing.

So, this energy is maximum when the capacitor is fully discharged. This happens at timet=T/4.

Hence, the value of time is t=T/4.

04

b) Calculation of the time at which the magnetic flux is maximum

The magnetic flux through the inductor is also maximum att=T/4since the energy is maximum at this time.

Hence, the value of time is t=T/4.

05

c) Calculation of the time at which the rate of current is maximum

Then the current through the circuit starts flowing and goes on increasing as the capacitor starts charging again. The current rises till the capacitor is charged fully but with opposite polarity. This occurs at timet=T/2.

Hence di/dt, is maximum at time t=T/2.

06

d) Calculation of the time at which the EMF is maximum

The EMF of the circuit is also maximum at the time, when the current flow is maximum. Hence, the EMF is maximum at T/2.

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Most popular questions from this chapter

(a) Does the phasor diagram of Fig. 31-26 correspond to an alternating emf source connected to a resistor, a capacitor, or an inductor? (b) If the angular speed of the phasors is increased, does the length of the current phasor increase or decrease when the scale of the diagram is maintained?

An ac voltmeter with a large impedance is connected in turn across the inductor, the capacitor, and the resistor in a series circuit having an alternating emf of 100V (RMS); the meter gives the same reading in volts in each case. What is this reading?

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Figure 31-36 shows an ac generator connected to a 鈥渂lack box鈥 through a pair of terminals. The box contains an RLC circuit, possibly even a multiloop circuit, whose elements and connections we do not know. Measurements outside the box reveal that(t)=(75.0V)sin(dt)and i(t)=(1.20A)sin(dt+42.0).

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