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# Assignment of electromagnetic induction and alternating current

## This assignment of electromagnetic induction and alternating current contain long answer type questions ( derivation and reasoning type questions. )

LONG ANSWER TYPE QUESTIONS OF ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENT

Q1. Explain with the help of a labelled diagram, the principle and working of an ac generator. Write the expression for the emf generated in the coil in terms of speed and rotation. Can the current produced by an ac generator be measured with a moving coil galvanometer ?

OR

Describe briefly , with the help of a labelled diagram, the basic elements of an ac generator. State its underlying principle. Show diagrammatically how an alternating emf is generated by a loop of wire rotating in a magnetic field. Write the expression for the instantaneous value of the emf induced in the rotating loop.

OR

State the working of ac generator with the help of a labelled diagram . the coil of an ac generator having N turns, each of area A, is rotated with a constant angular velocity ω. Deduce the expression for the alternating emf generated in the coil. What is the source of energy generation in this device?

Q2. derive an expression for impedance of an a.c. circuit consisting of an inductor and a resistor.

Q3. (a)State the condition for resonance to occur in series LCR a.c. circuit  and derive an expression for resonant frequency.

(b) Draw a plot showing the variation of the peak current (im)with frequency of the a.c. source used. Define the quality factor Q of the circuit.

Q4. Define the term capacitive reactance. Show graphically the variation of capacitive reactance with frequency of applied alternating voltage.

An ac voltage  V=V0 sin ωt is applied across a pure capacitor of capacitance C. Find an expression for current flowing through it. Show mathematically the current flowing through it leads the applied voltage by angle π/2.

Q5. Explain the term inductive reactance. Show graphically the variation of inductive reactance with frequency of the applied alternating voltage.

An ac voltage  V=V0 sin ωt is applied across a pure inductor of inductance L. Find an expression for current i, flowing in the circuit . Show mathematically the current flowing through it lags behind the applied voltage by phase angle π/2. Also draw (i) phasor diagram  (ii) graphs of V an I versus ωt for the circuit.

Q6. Derive an expression for (i)induced current when a conductor of length l is moved with a uniform velocity v. normal to a uniform magnetic field B. Assume the resistance of conductor to be R.

Q7. (a)What is induced emf ? write Faraday’s law of electromagnetic induction. Express it Mathematically.

(b) A conducting rod of length l with one end pivoted, is rotated with a uniform angular speed ω in a vertical plane, normal to a uniform magnetic field B. deduce an expression for the emf induced in this rod.

If resistance of rod is R, what is the current induced in it.

Q8. A coil of number of turns N, Area A is rotated at a constant angular speed ω in a uniform magnetic field B and conducted to a resistor R. Deduce the expression for

(i)Maximum emf induced in the coil.

(ii) Power dissipation in the coil .

Q9. (a)Describe briefly, with the help of a labeled diagram, the working of a step up transformer.

(b) Write any two source of energy loss in a transformer.

(c) A set up Transformer converts a low voltage into high voltage. Does it not violate the principle of conservation of energy? Explain.

OR

Draw a schematic Diagram of a set up transformer. Explain its working principle . Deduce the expression for the secondary to primary voltage in turms of number of turns in the two coils. In an ideal transformer, how is this ratio related to the current in the two coils?

How is the transformer used in large scale transmission and distribution of electrical energy over long distances?

Q10. An ac source of voltage V=Vm sin ωt is connected one by one, to three circuit elements X,Y and Z. It is observed that the current flowing in them.

(a) is in the phase with applied voltage for element X.

(b) lags the applied voltage, in phase, by angle π/2 for element Y.

(c) leads the applied voltage in phase by angle π/2.

Identify the three circuit elements.

Find an expression for for the current flowing in the circuit, when the same ac source is connected across a series combination of the elements X,Y and Z.

If the frequency of the applied voltage is varied, set up the condition of the frequency when the current amplitude in the circuit is maximum. Write expression for this current amplitude.

Q11. (a)What is impedance?

(b) A series LCR circuit is connected to an ac source having voltage V=V0 sin ωt. Derive an expression for the impedance, instantaneous current and its phase relationship to the applied voltage. Find the expression for the resonant frequency

OR

(a) ac source having voltage V=V0 sin ωt is connected to a series combination of L, C and R. Use the phasor diagram to obtain expression for impedance of the circuit and phase angle between voltage and current. Find the condition when the current will be in phase with the voltage. What is the circuit in this condition called?

(b)In a series LR circuit XL = R and power factor of the circuit is P1. When capacitor with capacitance C such that XL=XC is put in series, the power factor becomes P2 calculate P1/P2 .

Q12. Derive Expression for self inductance of a long air- cored solenoid of length l, cross- sectional area A and having number of turns N.

Q13. What do mean by mutual inductance of two nearby coils ? Find an expression for mutual inductance of two co-axial solenoid.

OR

(a)Define mutual inductance and write its SI units.

(b)Derive an expression for the mutual inductance of two long co – axial solenoid of same length wound one over the other.

(c)In an experiment, two coils C1 an C2 are placed   close to each other. Find out the expression for the emf induced in the coil C1 due to change in the current through coil C2.

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