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Alternating Current question

2022 · 29 Jul · Shift 1 · Q60
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Alternating Current question

2022 · 29 Jul · Shift 1 · Q60

JEE MainPhysicsAlternating CurrentMCQ+4 / −1
An alternating emf E=440sin⁡100πt\mathrm{E}=440 \sin 100 \pi \mathrm{t}E=440sin100πt is applied to a circuit containing an inductance of 2πH\frac{\sqrt{2}}{\pi} \mathrm{H}π2​​H. If an a.c. ammeter is connected in the circuit, its reading will be :
  1. A
    4.4 A
  2. B
    1.55 A
  3. C
    2.2 A
  4. D
    3.11 A
View written solutionFree

Correct answer: C

  1. Given alternating emf

    E=440sin⁡(100πt)E = 440\sin(100\pi t)E=440sin(100πt)

    Comparing with the standard form

    E=E0sin⁡(ωt)E = E_0\sin(\omega t)E=E0​sin(ωt)

    we get:

    E0=440 V,ω=100π rad/sE_0 = 440\text{ V}, \qquad \omega = 100\pi\text{ rad/s}E0​=440 V,ω=100π rad/s

  2. Given inductance

    L=2π HL = \frac{\sqrt{2}}{\pi}\text{ H}L=π2​​ H

  3. Inductive reactance

    For a pure inductor,

    XL=ωLX_L = \omega LXL​=ωL

    Substituting values:

    XL=(100π)(2π)=1002 ΩX_L = (100\pi)\left(\frac{\sqrt{2}}{\pi}\right) = 100\sqrt{2}\,\OmegaXL​=(100π)(π2​​)=1002​Ω

  4. Peak current

    For a pure inductive circuit,

    I0=E0XLI_0 = \frac{E_0}{X_L}I0​=XL​E0​​

    So,

    I0=4401002=4.42 AI_0 = \frac{440}{100\sqrt{2}} = \frac{4.4}{\sqrt{2}}\text{ A}I0​=1002​440​=2​4.4​ A

  5. RMS current

    An a.c. ammeter reads the rms current:

    Irms=I02I_{\text{rms}} = \frac{I_0}{\sqrt{2}}Irms​=2​I0​​

    Therefore,

    Irms=4.42⋅2=4.42=2.2 AI_{\text{rms}} = \frac{4.4}{\sqrt{2}\cdot \sqrt{2}} = \frac{4.4}{2} = 2.2\text{ A}Irms​=2​⋅2​4.4​=24.4​=2.2 A

  6. Match with options

    2.2 A\boxed{2.2\text{ A}}2.2 A​

    So the correct option is C.

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