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please answer this
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Asked by Prashant DIGHE | 27 Jan, 2020, 10:41: PM
answered-by-expert Expert Answer
current i(t) as a function of time in series LR circuit is given by
 
begin mathsize 14px style i left parenthesis t right parenthesis space equals space i subscript o space e to the power of bevelled fraction numerator negative t over denominator t subscript c end fraction end exponent space end style
where tc = L/R , is time constant of LR circuit and io = E/R , is saturation current.
E is emf of battery
 
charge dq drawn from battery for small time dt is given by,  dq = i(t) dt
 
Hence charge q drawn from battery from t=0 to t=tc is given by
 
begin mathsize 14px style q space equals space integral d q space equals space i subscript o integral subscript 0 superscript t subscript c end superscript left parenthesis 1 space minus space e to the power of bevelled fraction numerator negative t over denominator t subscript c end fraction end exponent space right parenthesis space d t space equals space fraction numerator i subscript o t subscript c over denominator e end fraction space equals 1 over e space cross times E over R cross times L over R space equals space fraction numerator E space L over denominator R squared space e end fraction end style
Answered by Thiyagarajan K | 28 Jan, 2020, 09:28: AM

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