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Consider the four circuits are shown in the figure, each consisting of a battery, a switch, a light bulb a resistor, and either a capacitor or an inductor. Assume the capacitor has a large capacitor and the inductor has a large inductance but no resistance. The light bulb has high efficiency. glowing whenever it carries electric current. (i) Describe what the light bulb does in each of circuits (a) through (d) after the switch is thrown closed. (ii) Describe what the light bulb does in each of circuits (a) through (d) when, having been closed for a long time interval, the switch is opened.

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Manoj Pandey
Manoj PandeyLv10
29 Jan 2021

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions


In the circuit in the figure above, the emf equals 5.63 V and hasnegligible internal resistance. The capacitance equals 1.31 µF andthe resistance equals 1.82 MΩ. Switch S has been closed for a longtime. Switch S is opened. After a time interval equal to one timeconstant of the circuit has elapsed, find the following:

(a) the charge on the capacitor plate on the right (in µC)
(b) the rate at which the charge is increasing (in µC/s)
(c) the current (in µC/s)
(d) the power supplied by the battery (in µW)
(e) the power delivered to the resistor (in µW)
(f) the rate at which the energy stored in the capacitor isincreasing (in µW)

1) Which one of the following quantities remains constant for a given LC circuit?
a) the energy stored in the capacitor
b) the sum of the energy stored in the capacitor and that in the inductor
c) the energy dissipated in the circuit
d) the energy stored in the inductor
e)the energy stored in the current flowing in the circuit
 
2)Which of the following best describes the term forced oscillations?
a) oscillations that occur in the windings of the inductor within an RLC circuit
b) oscillations that occur at the natural frequency of the circuit
c) oscillations requiring an applied force
d) oscillations that occur within the battery of an RLC circuit
e) oscillations that occur at a frequency other than the natural frequency of the circuit
 
3)An alternating current is set up in an RLC circuit. For which of the following circuit elements are the current and voltage in phase?
a) inductor only
b) capacitor only
c) inductor, resistor, and capacitor
d) resistor only
e) resistor and capacitor only
 
4)For an RLC circuit in the limit of very high frequency, what is the effective behavior of the capacitor and the inductor in the circuit?
a) The inductor acts like a very small resistance and the capacitor acts like a very small resistance.
b) The inductor acts like a very large resistance and the capacitor acts like a very small resistance.
c) The inductor acts like a very small resistance and the capacitor acts like a very large resistance.
d) The inductor acts like a very large resistance and the capacitor acts like a very large resistance.
 
5)Which of the following statements concerning resonance in an RLC circuit is true?
a) At the resonant frequency, the rms current is at a minimum and the impedance is at a maximum.
b) At the resonant frequency, the rms current is at a maximum and the impedance is at a minimum.
c) At the resonant frequency, the rms current is at a minimum and the impedance is at a minimum.
d) At the resonant frequency, the rms current is at a maximum and the impedance is at a maximum.
 
6)In a well-designed transformer with an iron core, the secondary coil has twice as many turns as the primary coil. Which one of the following statements concerning this transformer is true?
a) The flux that passes through each turn of the primary coil is twice the flux that passes through each turn of the secondary coil.
b) This is a step down transformer because the current in the secondary coil is less than that in the primary coil.
c) This kind of transformer is typically used between a power transmission line and a residence.
d) The induced emf generated in the secondary coil is twice as large as that generated in the primary coil.
e) The effect of the iron core is to reduce the magnetic field passing through the coils.

In a circuit containing only resistors, the basic (though notnecessarily explicit) assumption is that the current reaches itssteady-state value instantly. This is not the case for a circuitcontaining inductors. Due to a fundamental property of an inductorto mitigate any "externally imposed" change in current, the currentin such a circuit changes gradually when a switch is closed oropened.
Consider a series circuit containing a resistor of resistance andan inductor of inductance connected to a source of emf andnegligible internal resistance. The wires (including the ones thatmake up the inductor) are also assumed to have negligibleresistance.
Let us start by analyzing the process that takes place after switchis closed (switch remains open). In our further analysis, lowercaseletters will denote the instantaneous values of various quantities,whereas capital letters will denote the maximum values of therespective quantities.
Note that at any time during the process, Kirchhoff's loop ruleholds and is, indeed, helpful:
.
Part A
Immediately after the switch is closed, what is the current in thecircuit?
Hint A.1
How to approach the problem
Hint not displayed
ANSWER:

zero
Answer not displayed
Part B
Immediately after the switch is closed, what is the voltage acrossthe resistor?
Hint B.1
Ohm's law
Hint not displayed
ANSWER:

zero
Answer not displayed
Part C
Immediately after the switch is closed, what is the voltage acrossthe inductor?
Hint C.1
A formula for voltage across an inductor
Hint not displayed
ANSWER:

zero
Answer not displayed
Part D
Shortly after the switch is closed, what is the direction of thecurrent in the circuit?
ANSWER:
clockwise
counterclockwise
There is no current because the inductor does not allow the currentto increase from its initial zero value.
Answer not displayed
Part E
Shortly after the switch is closed, what is the direction of theinduced EMF in the inductor?
ANSWER:
clockwise
counterclockwise
There is no induced EMF because the initial value of the current iszero.
Answer not displayed
Part F
Eventually, the process approaches a steady state. What is thecurrent in the circuit in the steady state?
ANSWER:





Answer not displayed
Part G
What is the voltage across the inductor in the steady state?
Hint G.1
Induced EMF and current
Hint not displayed
ANSWER:
zero




Answer not displayed
Part H
What is the voltage across the resistor in the steady state?
ANSWER:
zero




Answer not displayed
Part I
Now that we have a feel for the state of the circuit in its steadystate, let us obtain the expression for the current in the circuitas a function of time. Note that we can use the loop rule (goingaround counterclockwise):
.
Note as well that and . Using these equations, we can get, aftersome rearranging of the variables and making the subsitution,
.
Integrating both sides of this equation yields
.
Use this last expression to obtain an expression for . Rememberthat and that .
Express your answer in terms of , , and . You may or may not needall these variables. Use the notation exp(x) for .
ANSWER:
=
Answer not displayed
Part J
Just as in the case of R-C circuits, the steady state here is neveractually reached: The exponential functions approach their limitsasymptotically as . However, it usually does not take very long forthe value of to get very close to its presumed limiting value. Thenext several questions illustrate this point.
Note that the quantity has dimensions of time and is called thetime constant (you may recall similar terminology applied to R-Ccircuits). The time constant is often denoted by . Using , one canwrite the expression

as
.
Find the ratio of the current at time to the maximum current.
Express your answer numerically, using three significantfigures.
ANSWER:
=
Answer not displayed
Part K
Find the time it takes the current to reach 99.999% of its maximumvalue.
Express your answer numerically, in units of . Use threesignificant figures.
ANSWER:
=
Answer not displayed

Part L
Find the time it takes the current to reach 99.999% of its maximumvalue. Assume that ohms and millihenrys.
Express your answer in seconds, using three significantfigures.
ANSWER:
=
Answer not displayed
seconds
Part M
Find the time it takes the current to reach 99.999% of its maximumvalue. Assume that ohms and henrys.
Express your answer in seconds, using three significantfigures.
ANSWER:
=
Answer not displayed
seconds
Part N
What fraction of the maximum value will be reached by the currentone minute after the switch is closed? Again, assume that ohms andhenrys.
Use three significant figures in your answer.
ANSWER:
=
Answer not displayed
Now consider a different situation. After switch has been closedfor a long time, it is opened; simultaneously, switch is closed, asshown in the figure. This effectively removes the battery from thecircuit.
The questions below refer to the time immediately after switch isopened and switch is closed.
Part O
What is the direction of the current in the circuit?
ANSWER:
clockwise
counterclockwise
The current is zero because there is no EMF in the circuit.
Answer not displayed
Part P
What is happening to the magnitude of the current?
ANSWER:
The current is increasing.
The current is decreasing.
The current remains constant.
Answer not displayed
Part Q
What is the direction of the EMF in the inductor?
ANSWER:
clockwise
counterclockwise
The EMF is zero because the current is zero.
The EMF is zero because the current is constant.
Answer not displayed
Part R
Which end of the inductor has higher voltage (i.e., to which end ofthe inductor should the positive terminal of a voltmeter beconnected in order to yield a positive reading)?
Hint R.1
How to approach the problem
Hint not displayed
ANSWER:
left
right
The potentials of both ends are the same.
The answer depends on the magnitude of the time constant.
Answer not displayed
Part S
For this circuit, Kirchhoff's loop rule gives
.
Note that , since the current is decreasing. Use this equation toobtain an expression for .
Hint S.1
Initial and final conditions
Hint not displayed
Hint S.2
Let us cheat a bit
Hint not displayed
Express your answer in terms of , , and . Use exp(x) for .
ANSWER:
=
Answer not displayed

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