Chapter 31 - Electromagnetic Oscillations and Alternating Current - Problems - Page 938: 50b

$f_d = 318~Hz$

We can write an expression for $V_R$: $V_R= I_R~R$ We can write an expression for $V_L$: $V_L= I_L~X_L$ We can equate the two expressions to find $f_d$: $V_R = V_L$ $I_R~R = I_L~X_L$ $R = X_L$ $R = \omega_d~L$ $R = 2\pi~f_d~L$ $f_d = \frac{R}{2\pi~L}$ $f_d = \frac{80.0~\Omega}{(2\pi)~(40.0\times 10^{-3}~H)}$ $f_d = 318~Hz$