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Alternating Current question

2011 · Q128
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Alternating Current question

2011 · Q128

NEETPhysicsAlternating CurrentMCQ+4 / −1
In the ac circuit an alternating voltage e = 2002200\sqrt 22002​sin100t volts is connected to a capacitor of capacity 1 μ\muμF. The r.m.s. value of the current in the circuit is
  1. A
    10 mA
  2. B
    100 mA
  3. C
    200 mA
  4. D
    20 mA
View written solutionFree

Correct answer: D

e0 = 2002200\sqrt 2 2002​ V, ω\omega ω = 100 rad s-1

The capacitive reactance is

XC = 1ωC=1100×1×10−6{1 \over {\omega C}} = {1 \over {100 \times 1 \times {{10}^{ - 6}}}}ωC1​=100×1×10−61​

The r.m.s. value of the current in the circuit is

ir.m.s = VrmsXC=e021ωC{{{V_{rms}}} \over {{X_C}}} = {{{{{e_0}} \over {\sqrt 2 }}} \over {{1 \over {\omega C}}}}XC​Vrms​​=ωC1​2​e0​​​

= 200221100×10−6{{{{200\sqrt 2 } \over {\sqrt 2 }}} \over {{1 \over {100 \times {{10}^{ - 6}}}}}}100×10−61​2​2002​​​

= 200 × 100 × 10–6 A = 2 × 10–2 A = 20 mA

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