When a resistor and an inductor in series are connected to a 240V supply current of 3A flows logging 370 behind the supply voltage, while voltage across inductor is 171V. Find the resistance of resistor, resistance and reactance of the inductor. -

$\emptyset = 37^0 ; I=3A ; V=240 v \\ V_{coil}=171 v \\ Z_{coil}=\dfrac{V_{coil}}{{I}}=57 \Omega \\ Z_{Total}=\sqrt{(R+r)^2+X_L^2} \rightarrow (1) \\ Z_{Total}= \dfrac V1= \dfrac{240}{3}=80 \Omega \\ \cos \emptyset=\dfrac{R_Tr}{Z_{Total}} \\ (R+r)=80 \cos 37 \\ R+r=63.891 \Omega$

Put in (1)

$Z_{Total}=\sqrt{(63.891)^2}+x^2_L \\ X_L=\sqrt{80^2-(63.891)^2} \\ X_L=48.145 \Omega \\ Zcoil=\sqrt{r^2+x^2_L} \\ Zcoil=\sqrt{57^2-(48.15)^2} \\ r=30.513 \Omega \\ R+r=63.891 \\ R+30.891=63.891 \\ R=63.891-30.513 \\ r=33.378 \Omega$