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STD 12 -7. Alternating current — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 -7. Alternating current4 Marks
MCQ
The angular frequency of alternating current in a $L-C-R$ circuit is $100\, rad / s$. The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.
  • A
    $0.8\, H$ and $150\, \mu F$
  • ✓
    $0.8\, H$ and $250\, \mu F$
  • C
    $1.33\, H$ and $250\, \mu F$
  • D
    $1.33\, H$ and $150\, \mu F$
✓

Answer

Correct option: B.
$0.8\, H$ and $250\, \mu F$
b
Current through $60 \Omega$ resistance $=\frac{15}{60}=\frac{1}{4} A$

thus capacitor current $=\frac{1}{4} A$

$\because V _{ C }= I X _{ C }$

$10=\frac{1}{4} \times \frac{1}{\omega C}$

$\therefore C =\frac{1}{40 \omega}=\frac{1}{4000}=250 \mu F$

Now,

current through $40 \Omega$ resistance $=\frac{20}{40}=\frac{1}{2} A$

thus current through inductor $=\frac{1}{2}-\frac{1}{4}=\frac{1}{4} A$

$V _{ L }= IX _{ L }=\frac{1}{4} \times \omega L$

$20=\frac{1}{4} \times 100 \times L$

$\Rightarrow L =0.8 H$

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