CBSE Class 12-science Answered

A coil of inductance 0.5H and resistance 100 ohms is connected to a 240V , 50 Hz A.C supply (a) what is the maximum current in the coil ? (b) what is the time lag between the voltage maximum and current maximum.

Asked by rutujasarangmehta | 15 Mar, 2016, 08:49: AM

Expert Answer

Given:

L = 0.50 H

R = 100 Ω

E_v = 240 V

v = 50 Hz

begin mathsize 14px style straight omega space equals space 2 πv space equals space 100 space straight pi space straight E subscript 0 space equals space square root of 2 straight E subscript straight v equals square root of 2 cross times 240 space straight V end style

begin mathsize 14px style left parenthesis straight a right parenthesis space straight I subscript 0 equals fraction numerator straight E subscript 0 over denominator square root of straight R squared plus straight omega squared straight L squared end root end fraction equals fraction numerator square root of 2 cross times 240 over denominator square root of 10 to the power of 4 plus left parenthesis 100 straight pi cross times 0.5 right parenthesis squared end root end fraction equals 1.82 space straight A end style

(b) In R-L circuit,

If E = E₀ cos ωt

I = I₀ cos (ωt-Φ)

At t = 0, E = E₀, i.e., voltage is maximum

begin mathsize 14px style At space straight t equals straight ϕ over straight omega comma space straight I equals straight I subscript 0 space cos space left parenthesis straight ϕ minus straight ϕ right parenthesis equals straight I subscript 0 cross times 1 comma space current space is space maximum therefore Time space lag space between space voltahe space maximum space and space current space maximum equals straight ϕ over straight omega As space space tanϕ equals ωL over straight R equals fraction numerator 2 straight pi cross times 50 cross times 0.50 over denominator 100 end fraction equals fraction numerator 22 over denominator 7 cross times 2 end fraction equals 1.571 straight ϕ equals tan to the power of negative 1 end exponent space left parenthesis 1.571 right parenthesis equals 57.5 degree equals fraction numerator 57.5 straight pi over denominator 180 end fraction radian therefore Time space lag equals straight ϕ over straight omega equals fraction numerator 57.5 straight pi over denominator 180 cross times 2 πv end fraction equals fraction numerator 57.5 over denominator 180 cross times 2 cross times 50 end fraction equals 3.19 cross times 10 to the power of negative 3 end exponent space sec end style

Answered by Faiza Lambe | 15 Mar, 2016, 09:59: AM

CBSE Class 12-science Answered

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