# Derive an expression for the current of a RLE rectifier

I'm trying to calculate an expression for this RLE rectifier:

simulate this circuit – Schematic created using CircuitLab

With

• $$\R=2 \Omega\$$
• $$\L=20 mH\$$
• $$\V_{DC}=100 V\$$
• $$\V_{m}=120 V\$$
• $$\f=60 Hz\$$

So to deduce the expression, I use the next function for the current: $$I(t\omega)=\frac{V_{m}}{Z}sin(t\omega-\phi)-\frac{V_{DC}}{R}+Ae^{\frac{-t\omega}{\omega\tau}}$$

based on the components given
$$I(t\omega)=21.8sin(t\omega-1.31)-50+Ae^{\frac{-t\omega}{3.77}}$$

and for A I use the idea that the initial current in the inductor is zero because it was zero before the diode started conducting and it cannot change instantaneously.

Then
$$I(0)=21.8sin(0-1.31)-50+Ae^{0}$$
yields that $$\A=71.06\$$

But in the book this appears as $$\A=75.3\$$
How must I calculate this A value?