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Electric Charges And Fields

Question
CBSEENPH12040068
Wired Faculty App

What is the value of inductance L for which the current is a maximum in a series LCR circuit with C =10μ F and ω = 1000 s-1

  • 100 mH

  • 1 mH

  • cannot bec calculated unless R is known

  • 10 mH

Solution

A.

100 mH

In resonance condition, maximum current flows in the circuit. 
Current in LCR series circuit.
straight i space equals space fraction numerator straight V over denominator square root of straight R squared space plus space left parenthesis straight X subscript straight L minus straight X subscript straight C right parenthesis squared end root end fraction
where V is rms value of current, R is resistance XL is inductive reactancea and Xc is capacititve reactance.
For  current to be maximum denominator should be minimum can be done, if
 XL = Xc 
This happens in resonance state of the circuit ie,
ωL space equals space 1 over ωC or straight L space equals space fraction numerator 1 over denominator straight omega squared straight C end fraction space.... space left parenthesis straight i right parenthesis Given comma space straight omega space equals space 1000 space straight s to the power of negative 1 end exponent comma space straight C space equals space 10 space straight mu space straight F space equals space 10 space straight x space 10 to the power of negative 6 end exponent Hence comma space straight L thin space space equals space fraction numerator 1 over denominator left parenthesis 1000 right parenthesis squared space straight x space 10 space straight x 10 to the power of negative 6 end exponent end fraction space equals space 0.1 space straight H equals space 100 space mH

Some More Questions From Electric Charges and Fields Chapter

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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