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In a particular R-L series circuit a voltage of 10V at 50 Hz produces a current of 700mA while the same
voltage at 75 Hz produces 500 mA. What are the values of circuit constants?

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1 Answer

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(i) Z = √(R2 + (2π x 50L)2) = √(R2 + 98696L2);

V = IZ or 10 = 700 x 10-3√(R2 + 98696L2)

√(R2 + 98696L2) = 10/700  × 10−3 = 100/7 

or R2 + 98696 L2 = 10000/49 ...(i)

(ii) In the second case Z = √(R2 + (2π x 75L)2) = √(R2 + 222066L2)

∴ 10 = 500 x 10-3√(R2 + 222066L2) i.e √(R2 + 222066L2) = 20 or R2 + 222066L2 = 400 (ii)

Subtracting Eq. (i) from (ii), we get 

222066 L2 − 98696 L2 = 400 − (10000/49) or 123370 L2 = 196 

or L = 0.0398 H = 40 mH. 

Substituting this value of L in Eq. (ii), we get, R2 + 222066 (0.398)2 = 400 

∴ R = 6.9 Ω

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