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A 100 
resistor
is connected to a 220 V, 50 Hz ac supply.
(a)
What is the rms value of current in the circuit?
(b)
What is the net power consumed over a fully cycle?
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(a) The peak voltage of an a.c. supply is 300 V.What is the rms voltage?
(b) The rms value of current in an ac circuit is 10 A. NN hat is the peak current?
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A 44 mH inductor is connected to 220 V. 50 Hzac supply. Determine the rms value of the current in the circuit.
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A 
capacitor is
connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current
in the circuit.
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In Exercise 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.
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Obtain the resonant
frequency 
of a series LCR
circuit with L = 2.0 H, C = 32 µF and R = 10 
. What is the
Q-value of this circuit?
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A charged 
capacitor is
connected 27 mH inductor. What is the angular frequency of free oscillations of
the circuit?
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Suppose the initial charge on the capacitor in Exercise 7.7 is 6 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?
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A series LCR
circuit with R = 20
, L = 1.5 H and
is connected to a
variable frequency 200 V ac supply. When the frequency of the supply equals the
natural frequency of the circuit, what is the average power transferred to the
circuit in one complete cycle?
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A radio can tune over
the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHZ).
If its LC circuit has an effective inductance of 
what must be the
range of its variable capacitor?
[Hint. For tuning, the
natural frequency i.e., the frequency of' free oscillations for the LC circuit
should be equal to the frequency of the radiowave.]
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Figure shows a
series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, 
R = 40
.
(a)
Determine the source frequency which drives the circuit in resonance.
(b)
Obtain the impedance of the circuit and the amplitude of current at the
resonating frequency.
(c)
Determine the rms potential drops across the three elements of the circuit.
Show that the potential drop across the LC combination is zero at the
resonating frequency.
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An LC circuit
contains a 20 mH inductor and a 
capacitor with an
initial charge of 10 mC. The resistance of the circuit is negligible. Let the
instant the circuit is closed be 
.
(a)
What is the total energy stored initially? Is it conserved during LC
oscillations?
(b)
What is the natural frequency of the circuit?
(e)
At what time is the energy stored
(i)
completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic
(i.e., stored in the inductor)?
(d)
At what times is the total energy- shared equally between the inductor and the
capacitor?
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A coil of
inductance 0.50 H and resistance 
is connected
to a 240 V, 50 Hz ac supply.
(a)
What is the maximum current in the coil?
(b)
What is the time lag between the voltage maximum and the current maximum?
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Obtain the answer (a) to (b) in Exercise 7.13 if the is connected to a high frequency supply (240 V, 10 kHz). Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the supply state?
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A 
capacitor in series
with a 
resistance is
connected to a 110 V, 60 Hz supply.
(a)
What is the maximum current in the circuit?
(b)
What is the time lag between the current maximum and the voltage maximum?
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Obtain the answers to (a) and (b) in Exercise 7.15 if the circuit is connected to a 110 V, 12 kHz supply. Hence, explain the statement that a capacitor is a conductor at very high frequencies. Compare this behaviour with that of a capacitor in a dc circuit after the steady state.
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Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements. L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified in Exercise 7.11 for this frequency.
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A circuit
containing a 80 mH inductor and a 
capacitor in series
is connected to a 230 V, 50 Hz supply. The resistance of the circuit is
negligible.
(a)
Obtain the current amplitude and rms values.
(b)
Obtain the rms values of potential drops across each element.
(c)
What is the average power transferred to the inductor?
(d)
What is the average power transferred to the capacitor?
(e)
What is the total average power absorbed by the circuit? [?Average? implies
?averaged over one cycle?.]
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Suppose the circuit
in Exercise 7.18 has a resistance of 
. Obtain the
average power transferred to each element of the circuit, and the total power
absorbed.
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A series LCR
circuit with 
is connected to a
230 V variable frequency supply.
(a)
What is the source frequency for which current amplitude is maximum. Obtain
this maximum value.
(b)
What is the source frequency for which average power absorbed by the circuit is
maximum. Obtain the value of this maximum power.
(c)
For which frequencies of the source is the power transferred to the circuit
half the power at resonant frequency? What is the current amplitude at these
frequencies?
(d)
What is the Q-factor of the given circuit?
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Obtain the resonant
frequency and Q-factor of a series LCR circuit with 
, 
and 
. It is desired to
improve the sharpness of the resonance of the circuit by reducing its 'full
width at half maximum' by a factor of 2. Suggest a suitable way.
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Answer the following questions:
(a) In any ac circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit? Is the same true for rms voltage?
(b) A capacitor is used in the primary circuit of an induction coil.
(c) An applied voltage signal consists of a superposition of a dc voltage and an ac voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the dc signal will appear across C and the ac signal across L.
(d) A choke coil in series with a lamp is connected to a dc line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp's brightness. Predict the corresponding observations if the connection is to an ac line.
(e) Why is choke coil needed in the use of fluorescent tubes with ac mains? Why can we not use an ordinary resistor instead of the choke coil?
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pressure head is at
a height of 300 m and the water flow available is 
. If the turbine
generator efficiency is 60%, estimate the electric power available from the
plant 
.
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A small town with a
demand of 800 kW of electric power at 220 V is situated 15 km away from an
electric plant generating power at 440 V. The resistance of the two wire line
carrying power is 
per km. The town
gets power from the line through a 4000-220 V step-down transformer at a
sub-station in the town,
(a)
Estimate the line power loss in the form of heat.
(b)
How much power must the plant supply, assuming there is negligible power I, due
to leakage?
(c)
Characterise the step up transformer the plant.
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Do the same exercise as above with the replacement of the earlier transformer by a 40,000 —220 V step-down transformer (Neglect, as before, leakage losses though, this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred.
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question_answer26)
If the rms current in
a 50 Hz ac circuit is 5 A, the value of the current 1/300 seconds after its
value becomes zero is
(a) 
(b)
(c)
(d)
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question_answer27)
An alternating current
generator has an internal resistance 
and an
internal reactance 
. It is used to
supply power to a passive load consisting of a resistance and a reactance
. For maximum power to be delivered
from the generator to the load, the value of is
equal to
(a) zero (b)
(c)
(d)
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question_answer28)
When a voltage
measuring device is connected to AC mains, the meter shows the steady input voltage
of 220 V. This means
(a) input voltage can not be AC voltage, but a DC voltage
(b) maximum
input voltage is 220 V
(c)
the meter reads not 
but 
and is calibrated to read 
(d)
the pointer of the meter is stuck by some mechanical defect
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question_answer29)
To reduce the
reasonant frequency in an LCR series circuit with a generator
(a) the generator frequency should be reduced
(b) another capacitor should be added in parallel to the
first
(c) the
iron core of the inductor should be removed
(d)
dielectric in the capacitor should be removed
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question_answer30)
Which of the following
combinations should be selected for better tuning of an LCR circuit used for
communication?
(a) 
(b) 
(c) 
(d) 
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question_answer31)
An inductor of
reactance 1
and a resistor of 2are connected in series to the
terminals of a 6 V (rms) a.c. source. The power dissipated in the circuit is
(a) 8
W (b) 12 W
(c)14.4
W (d)18 W
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question_answer32)
The output of a
step-down transformer is measured to be 24 V when connected to a 12 watt light
blub. The value of the peak current is
(a) 
(b) 
(c)
2 A (d) 
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question_answer33)
As the frequency of an
ac circuit increases, the current first increases and then decreases.
What
combination of circuit elements is most
likely to
comprise the circuit ?
(a) Inductor and capacitor
(b) Resistor and inductor
(c) Resistor and capacitor
(d) Resistor, inductor and capacitor.
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question_answer34)
In an alternating
current circuit consisting of elements in series, the current increases on increasing
the frequency of supply. Which of the following elements are likely to
constitute
the circuit?
(a) Only resistor
(b) Resistor and an inductor
(c) Resistor and a capacitor
(d) Only a capacitor.
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question_answer35)
Electrical energy is
transmitted over large distances at high alternating voltages. Which of the
following statements is (are) correct?
(a) For a given power level, there is a lower current
(b) Lower current implies less power loss
(c) Transmission lines can be made thinner
(d) It is easy to reduce the voltage at the receiving end
using step-down transformers
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question_answer36)
For an LCR circuit,
the power transferred from the driving source to the driven oscillator is
(a) Here, the power factor 
(b) The driving force can give no energy to the
oscillator
(P = 0) in some cases
(c)
The driving force can not syphon out (P < 0) the energy out of oscillator
(d)
The driving force can take away energy out
of
the oscillator
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question_answer37)
When an AC voltage of
220 V is applied to the capacitor C
(a) the maximum voltage between plates is
220V
(b)
the current is in phase with the applied voltage
(c)
the charge on the plates is in phase with the applied voltage
(d)
power delivered to the capacitor is zero
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question_answer38)
The line that draws
power supply to your house from street has
(a) zero average current
(b) 220 V average voltage
(c) voltage and current out of phase by 90°
(d) voltage and current possibly differing in
phase 
such that 
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question_answer39)
If a LC circuit is considered analogous to a harmonically oscillating
spring block system, which energy of the LC circuit would be analogous to
potential energy and which one analogous to kinetic energy?
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question_answer40)
Draw the effective equivalent circuit of the circuit shown
in Fig. 4(EP).24, at very high frequencies and find the effective impedance.
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question_answer41)
Study the circuits (a) and (b) shown in Fig. 4(EP).26 and
answer the following questions.
(a) Under which conditions would the rms currents in the
two circuits be the same?
(b) Can the rms current in circuit (b) be larger than that
in (a)?
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question_answer42)
Can the instantaneous power output of an ac source ever be
negative? Can the average power output be negative?
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question_answer43)
In series LCR circuit, the plot of 
vs 
is
shown in Fig. 4(EP).27. Find the bandwidth and mark in the figure.
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question_answer44)
The alternating current in a circuit is described by the
graph shown in Fig. 4(EP).29. Show rms current in this graph.
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question_answer45)
How does the sign of the phase angle , by which the supply voltage
leads the current in an LCR series circuit, change as the supply frequency is
gradually increased from very low to very high values?
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question_answer46)
A device 'X' is connected to an a.c. source. The variation of
voltage, current and power in one complete cycle is shown in Fig.
4(EP).31.
(a) Which
curve shows power consumption over a full cycle?
(b)
What is the average power consumption over a cycle?
(c)
Identify the device 'X'.
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question_answer47)
Both alternating current and direct current are measured in
amperes. But how is the ampere defined for an alternating current?
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question_answer48)
A coil of 
henry
inductance and 1 ohm resistance is connected to 200 volt, 50 Hz ac supply. Find
the impedance of the circuit and time lag between max. alternating voltage and
current.
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question_answer49)
A 60 W load is connected to the secondary of a transformer
whose primary draws line voltage. If a current of 
A
flows in the load, what is the current in the primary coil? Comment on the type
of transformer being used.
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question_answer50)
Explain why the reactance provided by a capacitor to an
alternating current decreases with increasing frequency.
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question_answer51)
Explain why the reactance offered by an inductor increases
with increasing frequency of an alternating voltage.
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question_answer52)
An electrical device draws 2 kW power from AC mains [voltage
223 V (rms) = 
V ]. The current
differs (lags) in phase by
as compared
to voltage. Find (i) R, (ii) 
, and (iii) 
. Another device has twice the
values for R, 
and. How are the answers affected?
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question_answer53)
1 MW power is to be delivered from a power station to a
town 10 km away. One uses a pair of Cu wires of radius 
cm for this purpose. Calculate
the fraction of ohmic losses to power transmitted if (i) power is transmitted
at 220 V. Comment on the feasibility of doing this.
(ii) a
step-up transformer is used to boost the voltage to 11000 V, power transmitted,
then a step-down transformer is used to bring voltage to 220 V. 
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question_answer54)
Consider the LCR circuit shown in Fig. 4(EP).32. Find the
net current 
and the phase of . Show that 
. Find the impedence Z for this
circuit.
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question_answer55)
For an LCR circuit driven at frequency , the equation reads 
(i) Multiply the equation by and
simplify where possible.
(ii) Interpret each term physically.
(iii) Cast the equation in the form of a conservation of
energy statement.
(iv) Intergrate the equation over one cycle to find that
the phase difference between 
and must be acute.
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question_answer56)
In the LCR circuit shown in Fig. 4(EP).33, the ac driving
voltage is 
(i) Write down the equation of motion for
.
(ii) At 
the voltage source stops and R
is short circuited. Now write down how much energy is stored in each of L and
C.
(iii) Describe subsequent motion of charges.
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