## Alternating Current  Important Questions for CBSE Class 12 Physics AC Currents

1.Phasor The representation of AC current and voltage by rotating vectors is calle^ phasor and the diagram representing these phasors is known as phasor diagram. The length of the vector represents the maximum or peak value. The projection of the vectors on fixed axis gives the instantaneous value of alternating current and voltage.

2.In an AC Circuit Containing Resistance Only

Suppose a resistor of resistance R is connected to an AC source of emf with instantaneous value E is given by

3.In an AC Circuit Containing Capacitor Only

Suppose a capacitor with capacitance C is connected to an AC source with emf having instantaneous value E is given by

4. In an AC Circuit Containing Inductor Only

10 .L-C Oscillations
Consider the L-C circuit shown as below:

When the charged capacitor is connected with the inductor, current flows through the inductor and energy stored in the inductor in the form of magnetic field and capacitor discharges and vice-versa. In this way, energy oscillates between capacitor and inductor. If the circuit is not ideal oscillations finally die away.

### 1 Mark Questions

1.A reactive element in an AC circuit causes the current flowing

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### 2 Marks Questions

2.A capacitor C, a variable resistor R and a bulb B are connected in series to the AC mains in the circuit as shown. The bulb glows with some brightness. How will the glow of the bulb change if (i) a dielectric slab is introduced between the plates of the capacitor keeping resistance R to be the same (ii) the resistance R is increased keeping the same capacitance? [Delhi 2014]

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Ans.Refer to ans3

Ans Refer to ans3.

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7. In a series L-C-R circuit, obtain the  conditions under which (i) the impedance of circuit is minimum and (ii) wattless current flows in the circuit.                     [Foreign 2014]

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13.(i) The graphs (I) and (II) represent the  variation of the opposition offered by the circuit element to the flow of alternating current with frequency of the applied emf. Identify the circuit element corresponding to each graph.
(ii) Write the expression for the impedance offered by the series combination of the above two elements connected across the AC sources. Which will be ahead in phase in this circuit, voltage or current?

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14. An AC source of voltage V = Vm sin wt is applied across a series L-C-R Draw the phasor diagram for this circuit when the

• capacitative impedance exceeds the inductive impedance.
• inductive impedance exceeds the capacitative impedance. [All India 2008C]

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15. An AC source of voltage V = Vm sin wt is applied across a

• series R-C circuit in which the capacitative impedance is a times the resistance in the circuit.
• series R – L circuit in which the inductive impedance is b times the resistance in the circuit.

Calculate the value of the power factor of the circuit in each case.  [All India 2008C]

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### 3 Marks Questions

16. A voltage V = V0 sin wt is applied to a series L-C-R 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?  [All India 2014]

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19.A series L-C-R 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.  [All India 2012]

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21. An AC voltage V = V0 sin wt is applied across a pure inductor Obtain an expression for the current / in the circuit and hence obtain the

• inductive reactance of the circuit and
• the phase of the current flowing with respect to the applied voltage.  [All India 2010C]

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Observe the graphs carefully.

(i) State the relation between L and C values of the two circuits when the current in the two circuits is maximum.

(ii) Indicate the circuit for which

• power factor is higher
• quality factor Q is larger.

Give the reasons for each case.  [Delhi 2009C]

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Ans. Refer Q.no 26

28. When a given coil is connected to a 200 V DC source, 2 A current flows and when the same coil is connected to 200 V, 50 Hz AC source, only 1 A current flows in the circuit.

• Explain why the current decreases in the latter case?
• Calculate the self-inductance of the  coil used.                                                                         [Foreign 2008]

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31. What does the term ‘phasors’ in AC circuit analysis mean? An AC source of voltage, V = Vm sin wt is applied across a pure inductor of inductance L. Obtain an expression for the current I flowing in the circuit. Also draw the

• phasor diagram.
• graphs of V and I versus wt for this  circuit.          [Delhi 2008C]

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### 5 Marks Questions

33. (i) A series L-C-R circuit is connected to  an AC source of variable frequency. Draw a suitable phasor diagram to deduce the expressions for the amplitude of the current and phase angle.

(ii) Obtain the condition at resonance. Draw a plot showing the variation of current with the frequency of AC source for two resistances R1 and R2 (R1 > R2). Hence, define the quality factor Q and write its role in the tuning of the circuit. [Delhi 2014C]

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34. Derive an expression for the impedance of a series L-C-Rcircuit 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?  [Delhi 2011]

Ans.Refer to ans.19 and for resonance condition refer to ans. 30(b)
35. (i) What do you understand by  sharpness of resonance in a series L-C-R circuit? Derive an expression for O-factor of the circuit.

(ii) Three electrical circuits having AC sources of variable frequency are shown in the figures. Initially, the current flowing in each of these is same. If the frequency of the applied AC source is increased, how will the current flowing in these circuits be affected? Give the reason for your answer.

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36.  A series L-C-Rcircuit is connected to an AC source having voltage V = Vm sin wt Derive the expression for the instantaneous current I and its phase relationship to the applied voltage. Obtain the condition for resonance to occur. Define power factor. State the conditions under which it is

• maximum and
• minimum.       [All India 2010]

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Ans. (i) Refer to ans 12(i)

(ii) Refer to ans. 35 (i)

Quality factor depends on ohmic resistance of L-C-R Series.Ac and Inductance and Capacitance of L-C-R Series AC Circuit.

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