**Q1.** When are the voltage and current in LCR a.c. circuit in same phase?

Answer- When the frequency of a.c applied becomes equal to the natural frequency of the LCR circuit (resonance occur when X_{L}= X_{R}) the voltage and current comes in same phase

**Q2.** What is the power factor of an a.c. LCR circuit at resonance?

Answer- At resonance impedance Z=R. Power factor cosΦ = R/Z = R/R =1

**Q3.** An electronic test circuit produced a resonant curve of half power frequency points at 414 Hz and 436 Hz. If Q factor be 10, then find the resonant frequency of the circuit.

Answer- Resonant frequency = Q factor × Bandwidth. =10 x (436 – 414) = 220 Hz

**Q4. **In series resonant circuit, what is the effect of increase in resistance on bandwidth?

Answer- Bandwidth is proportional to the value of resistance so bandwidth increases on increasing the value of resistance.

**Q5.** What is phase angle between voltage and current in a series LCR circuit at resonance?

Ans- zero

**Q6.** Why series resonant circuit is also known as acceptor circuit?

Ans- when a number of frequencies are fed in a resonant circuit, it accepts only one frequency (equal to its natural frequency) and rejects all other frequencies.

**Q7.** When an LCR circuit is brought into resonance, the current in the circuit increases to a large value. Explain Why?

Answer- In resonance condition, the impedance of the circuit becomes minimum equal to R and so the current in the circuit rises to maximum value.

**Q8.** Draw a graph to show the variation of current with applied frequency of a.c in LCR circuit. Also mark the resonance frequency and current at resonance.

**Q9.** On what factor, for a given value of L and C, the selectivity / sharpness/ q-factor of a series LCR depend upon?

Answer- For a given value of L and C the selectivity / sharpness/ q-factor of a series LCR depend upon the RESISTANCE of the circuit.

**Q10.** At any resonant frequency, what voltage is measured across the two series reactive components?

Ans- At resonance X_{L} = X_{C} having phase difference of 180 degree, hence voltage across reactive component is zero. Ans-

**Q11.** What is main cause of noise of transformer?

Answer- Transformer noise is mainly produced due to magnetostriction in core which leads to periodical change of dimension of laminated sheet. Noise also generated in transformer due to cooling fans and vibration of core but magnetostriction is the main cause of transformer noise.

**Q12.** How humming sound in a transformer is reduced?

Answer 12-The transformer humming noise is coming by the mechanical vibration during the working time. The mechanical vibrations are reduced by the proper casing and assembling the transformer.

**Q13. **Can we use transformer to step up D.C. voltage? If not, why?

ANS – Magnetic flux linked with Primary coil does not vary with time so no Induced emf in secondary.

**Q14.** Why the core of Transformer is laminated?

Ans- To reduce eddy current loss. They are made up of thin laminated sheet & are insulated from each other. Finally, the solid structure is pressed to remove presence of air gap.

**Q15. **What is the frequency of DC?

Ans- zero

**Q16.** Define RMS value of A.C. Write its expression.

Ans- RMS value of A.C. over one complete cycle: It is defined as that magnitude of direct current which produces the same heating effect in a given resistance as the given alternating current. i.e.

I_{RMS }= I_{o} / (2) ½ = 0.707 I_{o }

**Q17.** What is the reactance of an inductor in a d.c. circuit?

Ans- For d.c. *w* = 0, therefore X_{L} = *w*L =0

**Q18. ** The instantaneous voltage from an a.c. source E= 300 Sin 314 t. What is the rms value of the voltage?

Ans- E_{rms} = E_{0} /√2 = 300/ √2= 300 x 0.707 = 212.10 volt.

**Q19.** What are the dimensions of √(LC)?

Ans- [M^{0} L^{0}T^{1}]

**Q20.** When does series LCR circuit have minimum impedance?

Ans- At resonance when X_{L }=X_{C } impedance Z is minimum.

**Q21. **Capacitor blocks D.C. Why?

Ans- For d.c. f=0, therefore X_{C }=1/2fC = ∞

**Q22. **What is meant by admittance of an a.c. circuit?

Ans- The reciprocal of the impedance of an a.c. circuit is called its admittance.

**Q23.** The instantaneous current from an a.c. source is I= 6sin 314t. What is the r.m.s. value of the current?

Ans- I _{rms = } I_{o} /√2 = 6/√2 = 3√2 amp

**Q24.** Show that resistance offered by an ideal inductor to the flow of direct current is zero.

Ans- For d.c., f=0; X_{L= }2πfL = 0.

**Q25. **What is the phase difference between the voltage and current in a LCR series circuit at resonance?

Ans- Phase diff between voltage and current at resonance is zero.

**Q26.** A capacitor blocks d.c. Explain why.

Ans- X_{c }= 1/2πfC, for d.c. f=0, therefore X_{c }= ∞.

**Q27. **What do you mean by the admittance of LCR circuit?

Ans- reciprocal of impedence.

**Q28. **What is the dimensional formula of √LC?

Ans- Time.

**Q29.** In a series LCR circuit, what is the value of power factor at resonance?

Ans- Unity .

**Q30.** The effective value of current in a 50 cycles a.c. circuit is 5A. What is the value of current 1/300 s after it is zero?

Ans- I = I_{o }Sinωt

=√2 × 5 sin2π × 50× (1/300)

=6.124 A

**Q31.** A coil has an inductive reactance of 160 ohm at frequency of 50 Hz. Calculate the self-inductance of the coil.

Ans- X_{L }=2πfL

L=160/2π × 50 = 0.51 H

**Q32.** The frequency of a.c. source is doubled. How do X_{L }and X_{c }get affected?

Ans- X_{L }= double X_{L}=2πfL

X_{c} = half X_{c}= 1/2πfC

**Q33.** Draw the graph showing the variation of reactance of a capacitor with frequency of an a.c. circuit.

**Q34.** Draw the graph showing the variation of reactance of an inductor with frequency of an a.c. circuit.

**Q35.** The electric mains in a house is marked as 220 V, 50 cps. Write down the equation for the instantaneous voltage.

Ans-E = E_{o} Sin(2πft)

E = (√2×220) sin 2π×50×t

E= 311 sin 100πt is the required equation

**Q36. **The peak value of e.m.f. in an a.c. is E_{o. }Write its average value over a complete cycle.

Ans- Zero

**Q37.** Which value of the current do you measure with an a.c. ammeter?

Ans- Root mean square value of current.

**Q38. **The divisions marked on the scale of an a.c. ammeter are not equally spaced. Why?

Ans- A.C. ammeter is constructed on the basis of heating effect of electric current. Heat produced varies as square of the current.

**Q39.** A reactive element in an a.c. circuit causes the current flowing to lead in phase by π/2 w.r.t. the applied voltage. Identify the element.

Ans- Capacitor.

**Q40.** A reactive element in an a.c. circuit causes the current flowing to lack in phase by π/2 w.r.t. the applied voltage. Identify the element.

Ans- Inductor

**Q41.** The electric current flowing in a wire in the direction from B to A is decreasing. Find out the direction of the induced current in the metallic loop kept above the wire as shown.

Ans- Anticlockwise

Q42. A bar magnet is moved in the direction indicated by the arrow between two coils PQ and CD. Predict the directions of induced current in the coils.

Ans- Anticlockwise

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