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Alternating Current question

2012 · Q90
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Alternating Current question

2012 · Q90

NEETPhysicsAlternating CurrentMCQ+4 / −1
The instantaneous values of alternating current and voltage in a circuit are given as

i=12i = {1 \over {\sqrt 2 }}i=2​1​ sin (100 π\piπt) ampere

e=12sin⁡(100πt+π3)e = {1 \over {\sqrt 2 }}\sin \left( {100\pi t + {\pi \over 3}} \right)e=2​1​sin(100πt+3π​) Volt

The average power in watts consumed in the circuit is
  1. A
    14{1 \over 4}41​
  2. B
    34{{\sqrt 3 } \over 4}43​​
  3. C
    12{1 \over 2}21​
  4. D
    18{1 \over 8}81​
View written solutionFree

Correct answer: D

irms = i02=122=12{{{i_0}} \over {\sqrt 2 }} = {{{1 \over {\sqrt 2 }}} \over {\sqrt 2 }} = {1 \over 2}2​i0​​=2​2​1​​=21​ A

erms = e02=122=12{{{e_0}} \over {\sqrt 2 }} = {{{1 \over {\sqrt 2 }}} \over {\sqrt 2 }} = {1 \over 2}2​e0​​=2​2​1​​=21​ V

Average power consumed in the circuit,

P = irmserms cosϕ\phi ϕ

= (12)(12)cos⁡π3\left( {{1 \over 2}} \right)\left( {{1 \over 2}} \right)\cos {\pi \over 3}(21​)(21​)cos3π​ = 18{1 \over 8}81​ W

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