Answer
The required direct current is $~~1.84~A$
Work Step by Step
We can find an expression for the power when there is an alternating current:
$P = I_{rms}^2~R$
$P = (\frac{2.60}{\sqrt{2}})^2~R$
$P = (3.38)~R$
We can find a direct current that produces this power:
$P = I^2~R = 3.38~R$
$I = \sqrt{3.38}$
$I = 1.84~A$
Since the thermal energy produced in a resistor is proportional to the power, the required direct current is $~~1.84~A$
