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 elementof = 10.0 V and an internal resistance r_int = 0.05 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 11.5 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? Which of the following four circuit diagrams best represents the experiment described in this problem?

Explanation / Answer

Circuit A represents the experiment setup .The reason being the external resistance and battery resistance are in series and ammeter should also be in series to measure current in circuit.

Current in circuit = 11.5A

Battery source = 10 V

Total resistance of circuit = 10/11.5 = 0.87 Ohm

Internal resistance of battery = 0.05 ohm

Therefore, resistance of resistive coil, R = 0.87-0.05 = 0.82 Ohm

power dissipated across resistance = 11.52x0.82 = 108.4 Watts

Total energy required = 100kJ = 100000J

Total time required = 100000/108.4 = 922.5 seconds = 15.37 minutes

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