(i) Instantaneous Current $i_0:$ With RL load, the equation for instantaneous current $i_{0}$ can be obtained from Eq.2 (from Resistance Load equation) as

$$i_{0}(t)=\sum_{n=1,3,5, \ldots}^{\infty} \frac{2 E_{\mathrm{dc}}}{n \pi \sqrt{R^{2}+(n \omega L)^{2}}} \sin \left(n \omega t-\theta_{n}\right)-----(1)$$

Here, $Z_{n}=\sqrt{R^{2}+(n \omega L)^{2}}$ is the impedance offered by the load to the $n^{\text { th }}$ harmonic component, $\frac{2 E_{\mathrm{dc}}}{n \pi}$ is the peak amplitude of $n^{\text { th }}$ harmonic voltage, and

$$\theta_{n}=\tan ^{-1}\left(\frac{n \omega L}{R}\right)-----(2)$$

(ii) Fundamental Output Power: The output power at fundamental frequency $(n=1)$ is given by,

$$P_{rms}= E_{1rms} \cdot I_{1rms} \cdot cos \theta_1 = I^2_{1rms} \cdot R-----(3)$$

Where,

$ E_{1rms}$ = RMS value of fundamental output voltage.

$I_{1rms}$= RMS value of fundamental output current.

$\theta_{1}=\tan ^{-1}(\omega L / R)$

But $$\qquad I_{\operatorname{rms}}=\frac{2 E_{\mathrm{dc}}}{\sqrt{2} \cdot \pi \cdot \sqrt{R^{2}+(\omega L)^{2}}}-----(4)$$

$$P_{\mathrm{l}_{\operatorname{rms}}}=I_{\mathrm{1}_{\mathrm{rms}}}^{2} \cdot R=\left[\frac{2 E_{\mathrm{dc}}}{\pi \cdot \sqrt{2} \sqrt{R^{2}+(\omega L)^{2}}}\right]^{2} \cdot R-----(5)$$

$$=\left[\frac{4 E_{\mathrm{dc}}^{2} \cdot R}{2 \pi^{2}\left(R^{2}+\omega^{2} L^{2}\right)}\right]=\left[\frac{2 E_{\mathrm{dc}}^{2} \cdot R}{\pi^{2}\left(R^{2}+\omega^{2} L^{2}\right)}\right]-----(6)$$

Importance of fundamental power is that in many applications such as electric motor drives, the output power due to fundamental current is generally the useful power and the power due to harmonic current is dissipated as heat and increases the load dissipation.