To practice Problem-Solving Strategy 25.1 Power and Energy in Circuits. A device

Question

To practice Problem-Solving Strategy 25.1 Power and Energy in Circuits. A device for heating a cup of water in a car connects to the car's battery, which has an emf epsilon = 10.0 V and an internal resistance r_int = 0.04 Ohm. The heating element that is immersed in the cup of water is a resistive coil with resistance R. David wants to experiment with the device, so he connects an ammeter into the circuit and measures 12.0 A when the device is connected to the car's battery. From this, he calculates the time to boil a cup of water using the device. If the energy required is 100 kJ, how long does it take to boil a cup of water? Now that you have identified the known quantities, you can determine the most appropriate equations for solving the problem. Your target variable is t, the time needed to boil a cup of water using the electric device. EXECUTE the solution as follows Neglecting heat losses in the system, what is the amount of time t will it take to boil the water in the cup? Express your answer in minutes using three significant figures. t = minutes

Explanation / Answer

Part C) Here, I = E/(R + r)

=> 12 = 10/(R + 0.04)

=> R = 0.7933 ohm

=> time taken to boil water = W/P

                         = 100000/(12 * 12 * 0.7933)

                         =   14.589 minutes

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