(i) Z = √(R^{2} + (2π x 50L)^{2}) = √(R^{2} + 98696L^{2});

V = IZ or 10 = 700 x 10^{-3}√(R^{2} + 98696L^{2})

√(R^{2 }+ 98696L^{2}) = 10/700 × 10^{−3} = 100/7

or R^{2} + 98696 L^{2} = 10000/49 ...(i)

(ii) In the second case Z = √(R^{2} + (2π x 75L)^{2}) = √(R^{2} + 222066L^{2})

∴ 10 = 500 x 10^{-3}√(R^{2} + 222066L^{2}) i.e √(R^{2} + 222066L^{2}) = 20 or R^{2} + 222066L^{2} = 400 (ii)

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

222066 L^{2 }− 98696 L^{2} = 400 − (10000/49) or 123370 L^{2} = 196

or L = 0.0398 H = 40 mH.

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

∴ R = 6.9 Ω