chapter 7(alternating current)

1 N.K.Simplified Physics

Chapter-7(Alternating Current)

MCQ (1- mark) Question.1: The phase difference between the current and the voltage in series LCR circuit

at resonance is (a) (b) /2 (c) /3 (d) zero [CBSE-2020] Answer: (d) Question.2: The selectivity of a series LCR a.c. circuit is large, when [2020] (a) L is large and R is large (b) L is small and R is small (c) L is large and R is small (d) L = R Answer: (C) Question.3: The power factor of a series LCR circuit at resonance will be [2020] (a) 1 (b) 0 (c) 1/2 (d) 1/ 2 Answer: (a) Question.4: The selectivity of a series LCR a.c. circuit is large, when [2020] (a) L is large and R is large (b) L is small and R is small (c) L is large and R is small (d) L = R Very short answer questions (1- mark) Question.1: What is the impedance of a capacitor of capacitance C in an ac circuit using source of frequency n Hz? [CBSE-2020] Answer:

Question.2: What is the value of impedance of a resonant series LCR circuit? [CBSE-2020] Answer:

Question.3: In an ac circuit, the applied voltage and flowing current are E = E0 sin t and I

= I0 sin (t + /2 ) respectively. What is the average power consumed in one cycle in this circuit? [2020] Answer: Zero Question.4: An ac is passed through a series LCR circuit. What is the impedance of the circuit at resonance? [CBSE-2020] Answer: Question.5: A series combination of an inductor (L), capacitor (C) and a resistor (R) is

connected across an ac source of emf of peak value and angular frequency (). Plot a

graph to show variation of impedance of the circuit with angular frequency (). [CBSE-2020] Answer:

Question.5: An A.C. source with variable frequency is connected to a parallel plate capacitor. How will the displacement current be affected with the decrease in frequency of the source? Answer: The displacement current will decrease. 𝐻𝑖𝑛𝑡 ∶ − ( Question.6: Why is the use of a.c. Voltage preferred over d.c.voltage? Give two reasons. [2014]


Answer: 1. The generation of A.C. is economical. 2. A.C. can be easily converted in to D.C.

Question.7: predict the direction of induced current in a metal ring when the ring is moved towards a straight conductor with constant speed v. The conductor is carrying current I in the direction shown in the figure. [2012] Answer: Question.8: Define the term ‘wattless current’. [2011]

Answer: Watt less current: The current in a.c. circuits is said to be watt less if the average power consumed in the circuit is zero. Question.9: Mention the two characteristics properties of the material suitable for making core of a transformer. [2012] Answer: Two characteristics properties of material: (i) Low hysteresis loss (ii) Low coercivity. Short answer questions (2- marks) Question.1: (a) Explain the term ‘sharpness of resonance’ in ac circuit. (b) In a series LCR

circuit, VL = VC VR. What is the value of power factor for this circuit? [CBSE-2020] Answer: Sharpness of resonance is the sharpness of the peak of the resonance curve / a graph between current and angular frequency. The sharper or narrower the curve the narrower is the resonance or the resonance lasts over a very small range of frequencies / Q factor or quality factor is the measure of sharpness of curve. (b

Question.2: An ac source of emf V = V0 sin t is connected to a capacitor of capacitance C.

Deduce the expression for the current (I) flowing in it. Plot the graph of (i) V v/s. t, and

(ii) I v/s. t. [CBSE-2020] Answer:

Question.3: A resistor R and an inductor L are connected in series to a source of voltage V

= Vo sin t. The voltage is found to lead current in phase by /4. If the inductor is replaced

by a capacitor C, the voltage lags behind current in phase by /4. When L, C and R are connected in series with the same source, Find the: (i) average power dissipated and (ii) instantaneous current in the circuit. [CBSE-2020]


Answer: (i) Average power dissipated

(ii) Instantaneous Current

Question.4: A series LCR ac circuit has L = 2·0 H, C = 32 F and R = 10 . (a) At what angular frequency of ac will it resonate? (b) Calculate the Q value of the circuit. [2020] Answer: (a)

√

√

(b)

√

√

Question.5: State the underlying principle of a transformer. How is the large scale

transmission of electric energy over long distances done with the use of transformers?

[2012]

Answer: Transformer Principle: It is a device which converts high voltage AC into low

voltage AC and vice-versa. It is based upon the principle of mutual induction. When

alternating current is passed through a coil, an induced emf is set up in the

neighbouring coil. Transformers are used for transmission of electrical energy over long

distances.

It step up the output voltage of power plant using step up transformer which reduce the

current through cables and hence reduce resistive power loss. Then a step down

transformer is used at consumer end to step down the voltage.

Question.6: A light bulb is rated 100 W for 220 V ac supply of 50 Hz. Calculate: (i) The resistance of the bulb; (ii) The rms current through the bulb. [2012] Answer: (i)

(ii)

Question.7: An alternative voltage given by V = 140 sin 314t is connected across a pure resistor of 50Ω. Find (i) the frequency of the source. (ii) the rms current through the resistor. [2012] Answer: (i) Comparing with


(ii)

√

Short answer questions (3- marks) Question.1: The figure shows the graphical variation of the reactance of a capacitor with frequency of ac source. (a) Find the capacitance of the capacitor. (b) An ideal inductor has the same reactance at 100 Hz frequency as the capacitor has at the same frequency. Find the value of inductance of the inductor. (c) Draw the graph showing the variation of the reactance of this inductor with frequency. [CBSE-2020]

Answer:


Question.2: A resistance R and a capacitor C are connected in series to a source V = V0 sin

t. Find: (a) The peak value of the voltage across the (i) resistance and (ii) capacitor. (b) The phase difference between the applied voltage and current. Which of them is ahead? [2020] Answer: Peak value of

√

√

√

Question.3: A capacitor (C) and resistor (R) are connected in series with an ac source of voltage of frequency 50 Hz. The potential difference across C and R are respectively 120 V, 90 V, and the current in the circuit is 3 A. Calculate (i) the impedance of the circuit (ii) the value of the inductance, which when connected in series with C and R will make the power factor of the circuit unity. [2019] Answer:

√

√ for unit power factor

Question.4: The figure shows a series LCR circuit connected to a variable frequency 230 V source.

(a) Determine the source frequency which drives the circuit in resonance. (b) Calculate the impedance of the circuit and amplitude of current at resonance. (c) Show that potential drop across LC combination is zero at resonating frequency. [2019] Answer: (a)


√

√

(b)

√

√

√

(C)

Question.5: (i)When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero. (ii)A lamp is connected in series with an inductor and an AC source. What happens to the brightness of the lamp when the key is plugged in and an iron rod is inserted inside the inductor? Explain. [2016]

Answer: (i) For an ideal inductor,

ii) Brightness decreases. Because as iron rod is inserted inductance increases. Thus, current decreases and brightness decreases. Question.6: (a) Determine the value of phase difference between the current and the voltage in the given series LCR circuit. [CBSE-2015] (b) Calculate the value of the additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity. [CBSE-2015] Answer: Question.6: Explain with the help of a diagram, the working of a step-down transformer. Why is a laminated iron core used in a transformer? [CBSE-2020] Answer: (a)


(b) When an a.c. voltage is applied across the primary coil, the resulting a.c. current in the primary coil changes the magnetic flux linked with the secondary coil, as a result an emf is induced across the secondary coil. As the number of turns in the secondary coil is less than that in the primary coil in the step down transformer, the output voltage is less than the input voltage. (c) Use of laminated core :- Use of laminated sheets minimizes the eddy currents, hence the energy loss.

Question.7: An ideal inductor of /5 H inductance is connected to a 200 V, 50 Hz ac supply. (a) Calculate the rms and peak value of current in the inductor. (b) What is the phase difference between current through the inductor and the applied voltage? How will it change if a small resistance is connected in series with this inductor in the circuit? [CBSE-2020] Answer: (a)

√ (b) Phase difference is π/2 and it decreases. Question.8: A voltage V=V0sinωt is applied to a series LCR circuit. Derive the

expression for the average power dissipated over a cycle. Under what condition is (i) no

power dissipated even though the current flows through the circuit, (ii) maximum

power dissipated in the circuit ? [2014,2013]

Answer: AC power loss in LCR circuits:

⌈ ⌉

⌈ ⌉

⌈ ⌉

∫

⌈ ⌉

*∫ ∫

+

[ ] *∫

+

[ ]

√

√ [ ]

[ ]

(i) No power loss in LCR series circuit.


power in pure inductive or capacitive circuit, the phase difference between voltage and current is

[ ] = 0

(i) Maximum power loss in pure resistive circuit, the voltage and current are in same phase, [ ]

Question.9: A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit. Plot a graph to show the variation of current with frequency of the source, explaining the nature of its variation. [2012] Answer: Let an alternating emf V = V0 sin ωt is applied to a series combination of inductor L, capacitor C and resistance R. Since all three of them are connected in series the current through them is same. But the voltage across each element has a different phase relation with current. From

√[

√[

√[

√[

Phase angle of LCR series circuit:

At resonance


√

√

√

Where, f is known as resonance frequency.

With increase in frequency, current first increases and then decreases. At resonant frequency, the current amplitude is maximum. Long answer questions (5- marks) Question.1: (a) With the help of a labeled diagram, explain the working of a step-up transformer. Give reasons to explain the following: (i) the core of the transformer is laminated. (ii) Thick copper wire is used in windings. [CBSE-2020]

(b) A conducting rod PQ of length 20 cm and resistance 0·1 rests on two smooth parallel

rails of negligible resistance AA and CC. It can slide on the rails and the arrangement is positioned between the poles of a permanent magnet producing uniform magnetic field B = 0·4 T. The rails, the rod and the magnetic field are in three mutually perpendicular directions as shown in the figure. If the ends A and C of the rails are short circuited, find the (i) external force required to move the rod with uniform velocity v = 10 cm/s, and (ii) power required to do so [CBSE-2020] Answer:

When an alternating voltage is applied to the primary, the resulting current produces an alternating magnetic flux which links the secondary and induces an emf Induced emf across primary coil


(i) to minimise the eddy currents (ii) To reduce the heat loss (b) (i

Question.2: (a) Show that an ideal inductor does not dissipate power in an ac circuit. (b) The variation of inductive reactance (XL ) of an inductor with the frequency (f) of the ac source of 100 V and variable frequency is shown in the fig.

(i) Calculate the self-inductance of the inductor. (ii) When this inductor is used in series with a capacitor of unknown value and a resistor of , maximum power dissipation occurs in the circuit. Calculate the capacitance of the capacitor. [CBSE-2020]

Answer: (a)For ideal inductor phase difference between current and voltage is

Power dissipate in ideal inductor,

(b)

√

√

Question.2: (a) In a series LCR circuit connected across an ac source of variable frequency, obtain the expression for its impedance and draw a plot showing its variation with frequency of the ac source. [CBSE 2019]


(b) What is the phase difference between the voltages across inductor and the capacitor at resonance in the LCR circuit? [CBSE 2019] (c) When an inductor is connected to a 200 V dc voltage, a current of 1A flows through it. When the same inductor is connected to a 200 V, 50 Hz ac source, only 0.5 A current flows. Explain, why? Also, calculate the self-inductance of the inductor. [CBSE 2019] Answer: (a) AC Circuit with a pure capacitor, inductor and Resistor (LCR series circuit): The ac circuit in which inductor, capacitor and resistor are connected in series across ac source is known as LCR series circuit. From

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√[

√[

√[

(b)

√

√

Question.3: (a) Draw the diagram of a device which is used to decrease high ac voltage into a low ac voltage and state its working principle. Write four sources of energy loss in this device.

[CBSE 2019] (b) A small town with a demand of 1200 kW of electric power at 220 V is situated 20 km away from an electric plant generating power at 440 V. The resistance of the two wire line

carrying power is 0.5 per km. The town gets the power from the line through a 4000-


220 V step-down transformer at a sub-station in the town. Estimate the line power loss in the form of heat. [CBSE- 2019] Answer: (a)

Working Principle: When the alternating voltage is applied to the primary , the resulting current produces an alternating magnetic flux in secondary and induces an emf in it./It works on the mutual induction. Four sources of energy loss (i) Flux leakage between primary and secondary windings. (ii) Resistance of the windings. (iii) Production of eddy currents in the iron core. (iv) Magnetization of the core. (b) Total resistance of the line = length X resistance per unit length 𝛺 Current flowing in the line

[ CBSE- 2018]

Question.4: A device X is connected across an ac source of voltage V = V0 sin t. The

current through X is given as (

)

(a) Identify the device X and write the expression for its reactance. (b) Draw graphs showing variation of voltage and current with time over one cycle of ac, for X. (c) How does the reactance of the device X vary with frequency of the ac ? Show this variation graphically. (d) Draw the phasor diagram for the device X. [ CBSE- 2018] Answer:


Question.5: A device ‘X’ is connected to an ac source . The variation of voltage, current and power in one cycle is shown in the following graph : [ CBSE- 2017]

(a) Identify the device ‘X’. (b) Which of the curves A, B and C represent the voltage, current and the power consumed in the circuit ? Justify your answer. (c) How does its impedance vary with frequency of the ac source? Show graphically. (d) Obtain an expression for the current in the circuit and its phase relation with ac voltage. Answer: a) The device X is a capacitor b) Curve B voltage, Curve C current and Curve A power Reason: The current leads the

voltage in phase, by

, for a capacitor


Question.6: (a) Prove that an ideal capacitor in an a.c. circuit does not dissipate power. (b)

An inductor of 200 mH, capacitor of 400 f and a resistor of 10 are connected in series to ac source of 50 V of variable frequency. Calculate the (i) angular frequency at which maximum power dissipation occurs in the circuit and the corresponding value of the effective current, and (ii) value of Q-factor in the circuit. [Comp. 2017] Answer: (a) Power dissipates in ideal capacitor Phase difference between current and voltage is π/2

*

+

(b) Maximum power dissipate when voltage and current lie in same phase i.e. resonance condition

√

√

√

√

Question.7: (i) Draw a labelled diagram of a step-down transformer. State the principle

of its working.

(ii) Express the turn ratio in terms of voltages.

(iii) Find the ratio of primary and secondary currents in terms of turn ratio in an ideal

transformer.

(iv)How much current is drawn by the primary of a transformer connected to 220 V

supply when it delivers power to a 110 V - 550W refrigerator? [2016]

Answer: (i) Mutual induction, When the current flowing through the primary coil changes, an emf is induced in the secondary coil due to the change in magnetic flux linked with it.

(ii)


(iii)

(iv)

Question.8: (a) Explain the meaning of the term mutual inductance. Consider two concentric circular coils, one of radius and the other of radius placed coaxially with centers coinciding with each other. Obtain the expression for the mutual inductance of the arrangement. (b) A rectangular coil of area A, having number of turns N is rotated at' revolutions per. second in a uniform magnetic field B, the field being perpendicular to the coil. Prove that the maximum emf induced in the coil is [2016] Answer: (a) Mutual Inductance is the property of a pair of coils due to which an emf induced in one of the coils due to the change in the current in the other coil. Let a current flow through the outer circular coil. Then magnetic field due to coil

Magnetic flux passing through the coil 1

(b) The magnetic flux link with the coil

If The rate change of magnetic flux =

If the coil contain N turns For maximum emf,


Question.10: (a) Determine the value of phase difference between the current and the voltage in the given series LCR circuit.

(b) Calculate the value of the additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity. [2014] Answer: Phase angle

Let addition capacitance be connected

Question.11: In a series LCR circuit connected to an ac source of variable frequency and

voltage V=V0sinωt, draw a plot showing a current (I) with angular frequency (ω) for two

different values of resistance R1 and R2 (R1>R2). Write the condition under which the

phenomenon of resonance occurs. For which values of the resistance out of the two

curves, a sharp resonance is produced? Define Q- factor of the circuit and give its significance. [2013] Answer:

Resonance in LCR series circuit: When, Then LCR series circuit is said to be in electrical resonance. At resonance condition R = Z , the impedance is minimum and current in the circuit is maximum.


For resistance R2 curve produce sharp resonance. Quality Factor: The ratio of voltage across L and voltage across R is known as quality factor LCR circuit. Significance of the quality factor is quality of LCR series circuit. Question.12: A series LCR circuit with L = 4.0 H, C= 100μF and R = 60Ω is connected to a variable frequency 240 V source as shown in.

Calculate:

(i) The angular frequency of the source which derives the circuit at resonance. (ii) The current at the resonating frequency. (iii) The rms potential drop across the inductor at resonance. [2014]

Answer: (i)

√

√

(ii)At resonance Z = R

(iii) Question.13: Derive an expression for the impedance of a series LCR circuit connected to an AC supply of variable frequency. Plot a graph showing variation of current with the frequency of the applied voltage. Explain briefly how the phenomenon of resonance in the circuit can be used in the tuning mechanism of a radio or a TV set [2011] Answer: AC Circuit with a pure capacitor, inductor and Resistor (LCR series circuit): The ac circuit in which inductor, capacitor and resistor are connected in series across ac source is known as LCR series circuit. From

√[

√[

√[

√[


LCR series is used in the tuning of radio and TV set. In the tuning of radio and TV

frequency of radio set changes then frequency of radio set match with the frequency of electromagnetic wave due to resonance, radio set catch the signal.

Question.14: With the help of a labeled diagram, describe briefly the underlying

principle and working of a step up transformer. Write any two sources of energy loss in

a transformer.

A step up transformer converts a low input voltage into a high output voltage. Does it

violate law of conservation of energy? Explain. [2011]

Answer: Transformer: It is a device used to either increase or decrease the voltage of an a.c. supply. Principle: The principle of transformer depends on the mutual induction. Step up transformer: In the step up transformer primary coil consist of thick wire and less number of turns and secondary coil consist of thin wire and large number of turns. It is used to increase the voltage. Working: When an alternating voltage is applied to the primary coil of transformer then magnetic flux link with the (primary and secondary) coil will change and emf is induced in both coils. This induced emf is obtained across the secondary coil


Where, k is known as transformer ratio. There is no change in the frequency of A.C. In the transformer power remain same and efficiency of transformer is high.

Energy Losses in transformer: 1. Copper loss: Some energy is lost due to heating of copper wire. 2. Eddy current loss: Some energy lost due to eddy current in the iron core. This

energy loss can be reduced by using laminated core.

Transformer does not amplify the power so There is no violation of conservation energy in a step up transformer.

Question.15: (a) Show that in an a.c. circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase. (b) A horizontal straight wire of length L extending from east to west is hilling with speed v at right angles to the horizontal component of Earth’s magnetic field B. [2011] Answer: AC Circuit with a pure inductor: The AC circuit that contains only inductor only is known as pure inductive circuit.

If I is the current in the inductor and

is rate of change of current, the induced e.m.f.

V

[

]


In the pure inductive circuit current lags behind the voltage by

phase angle or voltage

leads the current by

phase angle.

(b)

(i) Direction of emf from south to north. (ii) Wire 1 is greater potential then wire .

chapter 7(alternating current)

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