A device for heating a cup of water in a car connects to the car\'s battery, whi

Question

A device for heating a cup of water in a car connects to the car's battery, which has an emf E = 10.0V and an internal resistance rint = 0.04? . 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 10.5A 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 100kJ , how long does it take to boil a cup of water?

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.

Explanation / Answer

current = V/Req

Req = R + r = R + 0.04

V = 10V

I = 10.5

thus

10.5 = 10 / R + 0.04

R = 0.91 ohm

Power supplied = I^2 R = 10.5 x 10.5 x .91 = 100.59 J/s

time required = 100 x 1000 / 100.59 = 994.13s = 16.57 min

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