Electricity question

Given $E= 10V(rms)$ , $f= 1kHz$ , $I= 29.94 mA(rms)$, $L= 21.28 V(p-p)$, series configuration RL. Solve for R and L.

The total impedance of the RL series circuit is $Z =R +i* \omega*L$

where $\omega = 2 \pi*F =2 \pi*10^3 =6.28*10^3 sec^(-1)$

The ohm law for the circuit is wrteen as E/I = absolute (Z) where absolute() is the absolute value of Z

$E/I = R^2 -\omega^2*L^2$

The ohm law for the coil L is $VL = |(i*\omega*L)|$ or $VL =\omega*L$

therefore one has the system of equations

$E/I = R^2 +\omega^2*L^2$

$VL =\omega*L$

$/0,02994 = R^2 -6.28*6.28*10^6*L^2$

$.28 =6.28*10^3 *L$

$L = 21.28/6.28*10^3 =0.0034$

$R = \sqrt {(789.9)}=28.1$ ohm