Through resistanceless leads, a capacitor of capacitance 12.0 is...

The time constant of the RC circuit is given by:

$\tau = RC = 1.00 \times 12.0 \times 10^{-6} = 12.0 \mu\text{s}$

The current in the circuit as a function of time is:

$I(t) = \dfrac{E}{R} e^{-t/\tau}$

At $t = 12.0 \mu\text{s}$, we have $t = \tau$. Substituting the values:

$I = \dfrac{6.00}{1.00} e^{-1} = \dfrac{6.00}{e} \approx 2.207 \text{ A}$

The total power delivered by the battery is the power supplied by its emf, which is given by:

$P = EI$

$P = 6.00 \times 2.207 \approx 13.24 \text{ W}$

Rounding to three significant figures, the power delivered is $13.2 \text{ W}$.