A coil with a resistance of 100 is connected across a battery...

The power generated by the coil is given by $P = \dfrac{V^2}{R}$.

Substituting $V = 6.0 \text{ V}$ and $R = 100 \Omega$, we get:

$P = \dfrac{(6.0)^2}{100} = 0.36 \text{ J s}^{-1}$

The heat required to raise the temperature of the coil is $Q = C \Delta T$.

Substituting $C = 4.0 \text{ J K}^{-1}$ and \Delta T = 15^{}^{{}^{\circ}} \text{C} = 15 \text{ K}, we get:

$Q = 4.0 \times 15 = 60 \text{ J}$

The time required to generate this heat is $t = \dfrac{Q}{P}$.

$t = \dfrac{60}{0.36} = \dfrac{1000}{6} \text{ s}$

Converting the time into minutes:

$t = \dfrac{1000}{6 \times 60} = \dfrac{100}{36} = 2.77 \text{ minutes}$

Rounding off to one decimal place, the time required is $2.8 \text{ minutes}$.