Alternating Current

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Question
CBSEENPH12039990

A 220 V input is supplied to a transformer. The output circuit draws a current 2.0 A at 440 V. If the efficiency of the transformer is 80%, the current drawn by the primary windings of the transformer is 

  • 3.6 A

  • 2.8 A

  • 2.5 A

  • 5.0 A

Solution

D.

5.0 A

Efficiency is defined as the ratio of output power and input power
i.e. straight eta percent sign space equals space straight P subscript out over straight P subscript in space straight x space 100 space equals space fraction numerator straight V subscript straight s straight i subscript straight s over denominator straight V subscript straight p straight i subscript straight p end fraction space straight x space 100

80 space equals space fraction numerator 2 space straight x space 440 over denominator 220 space straight x space straight i subscript straight p end fraction space straight x space 100

rightwards double arrow space straight i subscript straight p space equals space 5 space straight A

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Question
CBSEENPH12040074

A charged particle (charge q ) is moving n a circle of radius R with uniform speed v. The associated magnetic moment μ is given by:

  • qvR/2

  • qVR2

  • qVR2/2

  • qvR

Solution

A.

qvR/2

As revolving charge is equivalent to a current so
I = qf = q x ω/ 2π
But ω = v/R
Where R is radius of circle and v is uniform speed of charged particle, therefore,
I= qv/2πR
Now, magnetic moment associated with charged particle is given by 
μ = IA  = I x πR2
μ = qv/2 πR2
 = qvR/2


Question
CBSEENPH12040097

A coil of inductive reactance 31 Ω has a resistance of 8Ω. It is placed in series with a condenser of capacitative reactance 25Ω. The combination is connected to an a.c. soruce of 110 V. The power factor of the circuit is

  • 0.56

  • 0.64

  • 0.80

  • 0.33

Solution

C.

0.80

Power factor left parenthesis cos space straight ϕ right parenthesis is the ratio of resistance and impedance of a.c. circuit.
Power factor of a.c. circuit is given by
                             cos space straight ϕ space equals space straight R over straight Z                           ...(i)
where R is resistance employed and z the impedance of the circuit.
                                   straight Z equals space square root of straight R squared plus left parenthesis straight X subscript straight L minus straight X subscript straight C superscript 2 right parenthesis end root           ...(ii)
Eqs. (i) and (ii) meet to give,
                   cos space straight ϕ space equals space fraction numerator straight R over denominator square root of straight R squared plus left parenthesis straight X subscript straight L minus straight X subscript straight C right parenthesis squared end root end fraction                 ...(iii)
Given,       straight R space equals 8 straight capital omega comma space space straight X subscript straight L space equals space 31 straight capital omega comma space space straight X subscript straight C space equals space 25 straight capital omega
therefore space space space space space cos space straight ϕ space equals space fraction numerator straight R over denominator square root of left parenthesis 8 right parenthesis squared plus left parenthesis 31 minus 25 right parenthesis squared end root end fraction
space space space space space space space space space space space space space space space space space equals space fraction numerator 8 over denominator square root of 64 plus 36 end root end fraction
Hence comma space space cos space straight ϕ space equals space 0.80

Question
CBSEENPH12040083

A common emitter amplifier has a voltage gain of 50, an input impedance of 100 Ω and an output impedance of 200 Ω. The power gain of the amplifier is:

  • 500

  • 1000

  • 1250

  • 100

Solution

C.

1250

AC power gain is ratio of change in output power to the change in input power.
AC power gain
 equals space fraction numerator Change space in space output space power over denominator Change space in space input space power end fraction
space equals space fraction numerator increment straight V subscript straight c space straight x increment straight i subscript straight c over denominator increment straight V subscript straight i space straight x space increment straight i subscript straight b end fraction
space equals space open parentheses fraction numerator increment straight V subscript straight c over denominator increment straight V subscript straight i end fraction close parentheses space straight x space open parentheses fraction numerator increment straight i subscript straight c over denominator increment straight i subscript straight b end fraction close parentheses
space equals space straight A subscript straight v space straight x space straight beta subscript Ac space straight x space resistance space gain space open parentheses straight R subscript straight o over straight R subscript straight i close parentheses
Given comma space straight A subscript straight v space equals space 50 comma space straight R subscript straight o space equals space 200 space straight capital omega comma space straight R subscript straight i space equals space 100 space straight capital omega
Hence comma space 50 space equals space straight beta subscript AC space straight x space 200 over 100
straight beta subscript AC space equals space 25

Now comma space AC space power space gain space equals space straight A subscript straight C space straight x space straight beta subscript AC
space equals space 50 space straight x space 25
space equals space 1250

Question
CBSEENPH12040035

A galvanometer having a coil resistance of 60 Ω shows full-scale deflection when a current of 1.0 A passes through it. It can be converted into an ammeter to read currents up to 5.0 A by

  • putting in parallel a resistance of 240 Ω

  • putting in series a resistance of 15 Ω

  • putting in series a resistance of 240 Ω

  • putting in parallel a resistance of 15 Ω

Solution

D.

putting in parallel a resistance of 15 Ω

To convert a galvanometer to ammeter a small resistance is connected in parallel to the coil of the galvanometer.
Here G1 = 60 Ω, Ig = 1.0 A, I = 5 A
Ig G1 = (I - Ig) S

straight S space equals space fraction numerator straight I subscript straight g straight G subscript 1 over denominator straight I space minus straight I subscript straight g end fraction space equals space fraction numerator 1 over denominator 5 minus 1 end fraction space straight x space 60 space equals space 15 space straight capital omega
Putting 15 Ω resistance in parallel.

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