Here are the voltage and current shown for the primary winding of a transformer or an ideal inductor when the voltage is sinusodial.
My question is why the current is increasing when the voltage is decreasing as shown in the black box ? Its obvious that current should be increasing with increasing voltage and current should be decreasing with decreasing voltage but here the current is increasing for decreasing voltage.
It's obvious that into a resistor current increases with increasing voltage, and decreases with decreasing voltage, because that's how a resistor works, the current is governed by the voltage.
However, an inductor is not a resistor. The current in an inductor is governed not by the voltage, but by the time integral of the voltage
And the current decreases during the negative voltage cycles only.
What is the the reason behind all this ?
Because it's only in the negative half cycle that the time integral of the voltage decreases.
I suspect you're having problems with the concept of a time integral. Let's find something more familiar that's also a time integral.
Your credit card debt is the time integral of the rate at which you buy stuff online. If you keep buying stuff, your debt will keep increasing. It doesn't matter whether the rate at which you buy stuff is increasing, or decreasing (hey, I bought less stuff than last week!). As long as the rate is positive, like the voltage is positive, the debt or the inductor current will keep increasing. To get the debt or the current to decrease, the spend rate or the voltage must actually go negative, so sell some stuff and pay off some debt.