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**Exercise : ** Solutions of Questions on Page Number : **266**

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Q1 :
**
**

A 100 ÃŽÂ© 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 full cycle?

**Answer :**

Resistance of the resistor, *R* = 100
ÃŽÂ©

Supply voltage, *V* = 220 V

Frequency, *ÃŽÂ½***=** 50 Hz

**(a)** The rms value of current in the circuit is given as:

**(b)** The net power consumed over a full cycle is given as:

*P* = *VI*

= 220 × 2.2 = 484 W

Answer needs Correction? Click Here

Q2 :
**
**

**(a)** The peak voltage of an ac supply is 300 V. What is the
rms voltage?

**(b)** The rms value of current in an ac circuit is 10 A.
What is the peak current?

**Answer :**

**(a)** Peak voltage of the ac supply, *V*_{0} =
300 V

Rms voltage is given as:

**(b)** Therms value of current is given as:

*I* = 10 A

Now, peak current is given as:

Answer needs Correction? Click Here

Q3 :
**
**

A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

**Answer :**

Q4 :
**
**

A 60 ÃŽÂ¼F capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

**Answer :**

Q5 :
**
**

In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.

**Answer :**

Q6 :
**
**

Obtain the resonant frequency
*Ãâ€°**r* of a series *LCR*
circuit with *L* = 2.0 H, *C* = 32
ÃŽÂ¼F and *R* = 10
ÃŽÂ©. What is the *Q*-value of this
circuit?

**Answer :**

Q7 :
**
**

A charged 30 ÃŽÂ¼F capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

**Answer :**

Q8 :
**
**

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?

**Answer :**

Q9 :
**
**

A series *LCR* circuit with *R* = 20
ÃŽÂ©, *L* = 1.5 H and *C* = 35
ÃŽÂ¼F 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?

**Answer :**

Q10 :
**
**

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 200
ÃŽÂ¼H, what must be the range of its
variable capacitor?

[*Hint:* For tuning, the natural frequency i.e., the
frequency of free oscillations of the *LC* circuit should be
equal to the frequency of the radiowave.]

**Answer :**

Q11 :
**
**

Figure 7.21 shows a series *LCR* circuit connected to a
variable frequency 230 V source. *L* = 5.0 H, *C* =
80ÃŽÂ¼F, *R* = 40
ÃŽÂ©

**(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.

**Answer :**

Q12 :
**
**

An *LC* circuit contains a 20 mH inductor and a 50
ÃŽÂ¼F capacitor with an initial charge
of 10 mC. The resistance of the circuit is negligible. Let the
instant the circuit is closed be *t* = 0.

**(a)** What is the total energy stored initially? Is it
conserved during *LC* oscillations?

**(b)** What is the natural frequency of the circuit?

**(c)** 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?

**(e)** If a resistor is inserted in the circuit, how much
energy is eventually dissipated as heat?

**Answer :**

Q13 :
**
**

A coil of inductance 0.50 H and resistance 100 ÃŽÂ© 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?

**Answer :**

Q14 :
**
**

Obtain the answers (a) to (b) in Exercise 7.13 if the circuit 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 steady state?

**Answer :**

Q15 :
**
**

A 100 ÃŽÂ¼F capacitor in series with a 40 ÃŽÂ© 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?

**Answer :**

Q16 :
**
**

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.

**Answer :**

Q17 :
**
**

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.

**Answer :**

Q18 :
**
**

A circuit containing a 80 mH inductor and a 60 ÃŽÂ¼F 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'.]

**Answer :**

Q19 :
**
**

Suppose the circuit in Exercise 7.18 has a resistance of 15 ÃŽÂ©. Obtain the average power transferred to each element of the circuit, and the total power absorbed.

**Answer :**

Q20 :
**
**

A series *LCR* circuit with *L* = 0.12 H, *C* =
480 nF, *R* = 23 ÃŽÂ© 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?

**Answer :**

Q21 :
**
**

Obtain the resonant frequency and *Q*-factor of a series
*LCR* circuit with *L* = 3.0 H, *C* = 27
ÃŽÂ¼F, and *R* = 7.4
ÃŽÂ©. 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.

**Answer :**

Q22 :
**
**

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?

**Answer :**

Q23 :
**
**

A power transmission line feeds input power at 2300 V to a stepdown transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?

**Answer :**

Q24 :
**
**

At a hydroelectric power plant, the water pressure head is at a
height of 300 m and the water flow available is 100 m^{3}
s^{-1}. If
the turbine generator efficiency is 60%, estimate the electric
power available from the plant (g= 9.8 m
s^{-2}).

**Answer :**

Q25 :
**
**

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 0.5 ÃŽÂ© 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 loss due to leakage?

**(c)** Characterise the step up transformer at the plant.

**Answer :**

Q26 :
**
**

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?

**Answer :**

Physics : CBSE ** NCERT ** Exercise Solutions for Class 12th for ** Alternating Current ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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