Two metal wires of identical dimensions are connected in series

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 Multiple Choice QuestionsMultiple Choice Questions

171.

The electric and the magnetic field, associated with an electromagnetic wave, propagating along the +z - axis, can be represented by

  • left square bracket bold E space equals space straight E subscript straight o bold k with hat on top comma space bold B space equals space straight B subscript straight o space bold i with hat on top right square bracket
  • left square bracket bold E space equals space straight E subscript straight o bold j with hat on top comma space bold B space equals space straight B subscript straight o space bold j with hat on top right square bracket
  • left square bracket bold E space equals space straight E subscript straight o bold j with hat on top comma space bold B space equals space straight B subscript straight o space bold k with hat on top right square bracket
  • left square bracket bold E space equals space straight E subscript straight o bold j with hat on top comma space bold B space equals space straight B subscript straight o space bold k with hat on top right square bracket
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172.

A proton and an alpha particle both enter a region of uniform magnetic field B, moving at angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be

  • 4 MeV

  • 0.5 Mev

  • 1.5 MeV

  • 1.5 MeV

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173.

Two metal wires of identical dimensions are connected in series if σ1a nd σ2 are the conductivity of the metal wires respectively, the conductivity of the combination is 

  • fraction numerator 2 straight sigma subscript 1 straight sigma subscript 2 over denominator straight sigma subscript 2 space plus straight sigma subscript 2 end fraction
  • fraction numerator straight sigma subscript 1 space plus straight sigma subscript 2 over denominator 2 space straight sigma subscript 1 straight sigma subscript 2 end fraction
  • fraction numerator straight sigma subscript 1 space plus straight sigma subscript 2 over denominator straight sigma subscript 1 straight sigma subscript 2 end fraction
  • fraction numerator straight sigma subscript 1 space plus straight sigma subscript 2 over denominator straight sigma subscript 1 straight sigma subscript 2 end fraction


A.

fraction numerator 2 straight sigma subscript 1 straight sigma subscript 2 over denominator straight sigma subscript 2 space plus straight sigma subscript 2 end fraction

Net resistance of a metal wire having resistivity rho,

we have

straight R subscript 1 space equals space straight rho subscript 1 straight L over straight A
similarly comma

straight R subscript 2 space equals space straight rho subscript 2 straight L over straight A
Then comma space net space effective space resistance space of space two space metal space wires.
straight R subscript eq space equals space straight R subscript 1 space plus straight R subscript 2
rightwards double arrow space straight rho fraction numerator 2 straight L over denominator straight A end fraction space equals space straight rho subscript 1 straight L over straight A space plus straight rho subscript 2 straight L over straight A

rightwards double arrow space 2 straight rho space equals space straight rho subscript 1 space plus straight rho subscript 2
As comma space conductivity space straight sigma space equals space 1 over straight rho comma space we space have
2 over straight sigma space equals space 1 over straight sigma subscript 1 space plus space 1 over straight sigma subscript 2

rightwards double arrow 2 over straight rho space equals space fraction numerator straight sigma subscript 1 plus straight sigma subscript 2 over denominator straight sigma subscript 1 straight sigma subscript 2 end fraction
rightwards double arrow space Net space effective space conductivity space of space combined space wires comma

straight sigma space equals space fraction numerator 2 straight sigma subscript 1 straight sigma subscript 2 over denominator straight sigma subscript 1 plus straight sigma subscript 2 end fraction

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174.

An electron moves on a straight line path XY as shown. The abcd is a coil adjacent in the path of the electron. What will be the direction of the current, if any induced in the coil?

  • abcd

  • adcb

  • the current will reverse its direction as the electron goes past the coil

  • the current will reverse its direction as the electron goes past the coil

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175.

A galvanometer of resistance, G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged,the resistance to be put in series with the galvanometer is

  • fraction numerator straight S squared over denominator left parenthesis straight S space plus straight G right parenthesis end fraction
  • fraction numerator SG over denominator left parenthesis straight S plus straight G right parenthesis end fraction
  • fraction numerator straight G squared over denominator left parenthesis straight S space plus straight G right parenthesis end fraction
  • fraction numerator straight G squared over denominator left parenthesis straight S space plus straight G right parenthesis end fraction
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176.

A thermocouple force towards the conductor produces an emf of 40 μ V/oC in the linear range of temperature. A galvanometer of resistance 10 Ω whose sensitivity is 1μA/div, is employed with the thermocouple. The smallest value of temperature difference that can be detected by the system will be.

  • 0.5oC

  • 1oC

  • 0.1oC

  • 0.1oC

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177.

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency f Hz. The magnitude of magnetic induction at the centre of the ring is 

  • μoqf  / 2R

  • μoq / 2fR

  • μoq / 2πfR

  • μoq / 2πfR

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178.

A short bar magnet of magnetic moment 0.4 JT-1 is placed in a uniform magnetic field of 0.16T. The magnet is stable equilibrium when the potential energy is

  • -0.64 J

  • zero

  • -0.082 J

  • -0.082 J

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179.

A potentiometer circuit is set up as shown. The potential gradient across the potentiometer wire is k volt /cm and the ammeter, present in the circuit, reads 1.0 A when the two-way key is switched off. The balance points, when the key between the terminals (i) 1 and 2 (ii) 1 and 3, is plugged in, are found to be at lengths  l1 and l2 cm respectively. The magnitudes, of the resistor R and X, in ohm, are then, equal respectively, to

 

  • k (l2 -l1) and kl2

  • kl1 and k (l2-l1)

  • k (l2 - l1) and kl1

  • k (l2 - l1) and kl1

1223 Views

180.

A galvanometer has a coil of resistance 100 Ω and gives a full-scale deflection for 30 mA current. If it is to work as a voltmeter of 30 V range, the resistance required to be added will be

  • 900 Ω

  • 1800

  • 500 Ω

  • 500 Ω

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