A coil with a resistance of 100 is connected across a battery having an emf of 6.0 V . Assuming all the heat developed in the coil goes into raising its temperature, and given that the heat capacity of the coil is 4.0 J K ⁻¹ , determine the time required to increase the temperature of the coil by 15^ C .

Step-by-step solution

The power generated by the coil is given by P = V^2 R . Substituting V = 6.0 V and R = 100 , we get: P = (6.0)^2 100 = 0.36 J s ⁻¹ The heat required to raise the temperature of the coil is Q = C T . Substituting C = 4.0 J K ⁻¹ and T = 15^ C = 15 K , we get: Q = 4.0 15 = 60 J The time required to generate this heat is t = Q P . t = 60 0.36 = 1000 6 s Converting the time into minutes: t = 1000 6 60 = 100 36 = 2.77 minutes Rounding off to one decimal place, the time required is 2.8 minutes .