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 E = 10.0 V and an internal resistance rint = 0.04 Ω . 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?
The first thing we must do is calculate the external resistance (R) of the circuit, from the description we notice that it is a series circuit, by which the resistors are added
V = i (r + R)
We replace we calculate
r + R = V / i
R = v / i - r
R = 10/12 -0.04
R = 0.793 Ω
We calculate the power supplied
P = V i = I² R
P = 12² 0.793
P = 114 W
This is the power dissipated in the external resistance
We use the relationship, that power is work per unit of time and that work is the variation of energy
