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CBSE Class 12-science Answered

a 100 micro farad capacitor in series with a 40 ohms resistance is connected to a 110V , 60 Hz supply (a) what is the maximum current in the circuit (b) what is the time lag between the current maximum and voltage  maximum.
Asked by rutujasarangmehta | 15 Mar, 2016, 08:55: AM
answered-by-expert Expert Answer
Given:
C = 100 μF = 100 × 10-6 F = 10-4 F
R = 40 Ω
Ev = 110 volt
E0 =begin mathsize 14px style square root of 2 straight E subscript straight v equals square root of 2 cross times 110 space straight V end style
v = 60 Hz
ω = 2Πv = 120 Π rad/s
I0 = ?
In RC circuit, as 
begin mathsize 14px style straight Z space equals space square root of straight R squared plus straight X subscript straight C superscript 2 end root equals square root of straight R squared plus fraction numerator 1 over denominator straight omega squared straight C squared end fraction end root therefore straight I subscript 0 equals fraction numerator straight E subscript 0 over denominator square root of straight R squared plus fraction numerator 1 over denominator straight omega squared straight C squared end fraction end root end fraction equals fraction numerator square root of 2 cross times 110 over denominator square root of 1600 plus begin display style fraction numerator 1 over denominator left parenthesis 120 straight pi cross times 10 to the power of negative 4 end exponent right parenthesis squared end fraction end style end root end fraction equals 3.24 space amp end style
In RC circuit, voltage lags behind the current by phase angle Φ,
where
begin mathsize 14px style tanϕ equals fraction numerator 1 divided by ωC over denominator straight R end fraction equals 1 over ωCR equals fraction numerator 1 over denominator 120 straight pi cross times 10 to the power of negative 4 end exponent cross times 40 end fraction equals 0.6628 straight ϕ equals tan to the power of negative 1 end exponent left parenthesis 0.6628 right parenthesis equals 33.5 degree equals fraction numerator 33.5 straight pi over denominator 180 end fraction rad. Time space lag equals straight ϕ over straight omega equals fraction numerator 33.5 straight pi over denominator 180 cross times 120 straight pi end fraction equals 1.55 cross times 10 to the power of negative 3 end exponent space sec end style
Answered by Faiza Lambe | 15 Mar, 2016, 10:14: AM
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