A 6 V ideal battery, a 1 resistor, and a 2.0 resistor are connected in series. The 2.0 resistor is dipped into a calorimeter containing water. The heat capacity of the calorimeter together with the water is 2000 J K ⁻¹ . Determine the rise in the temperature of the water if the circuit is active for 15 minutes.

Step-by-step solution

Based on the problem description, the 6 V battery, the 1 resistor, and the 2.0 resistor are connected in series. The equivalent resistance of the circuit is: R_ eq = 1 + 2.0 = 3 The current flowing through the circuit is: I = V R_ eq = 6 3 = 2 A The power dissipated by the 2.0 resistor (which is inside the calorimeter) is: P = I^2 R = (2)^2 2.0 = 8 W The heat generated in the 2.0 resistor over a time t = 15 minutes = 15 60 s = 900 s is: H = P t = 8 900 = 7200 J The rise in temperature T of the calorimeter and water