An electric immersion heater normally takes 100 min to bring...

An electric immersion heater normally takes 100 min to bring cold water in a well-insulated container to a certain temperature, after which a thermostat switches the heater off. One day the line voltage is reduced by 6.00$\%$ because of a laboratory overload. How long does heating the water now take? Assume that the resistance of the heating element does not change.

An electric immersion heater normally takes 100 min to bring cold water in a well-insulated container to a certain temperature,
after which a thermostat switches the heater off. One day the line
voltage is reduced by 6.00$\%$ because of a laboratory overload. How long does heating the water now take? Assume that the resistance of the heating element does not change.

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Key Concepts

Energy and Heating Time Relationship

Heating time is directly related to the energy required to raise the temperature of a substance and inversely related to the power delivered by the heating device. When the power is reduced due to a lower voltage, the time required to supply the same amount of energy increases proportionally. This concept ties together the energy needed for heating and the power delivered by the electrical device.

Voltage Dependence of Power

Since the power in a resistive load depends on the square of the voltage, even a small percentage decrease in voltage leads to a larger percentage decrease in power. Understanding this quadratic relationship is essential when analyzing the behavior of devices under varying voltage conditions, as a reduction in voltage will significantly reduce the power output.

Electrical Power in Resistive Loads

This concept explains how the power delivered to a resistor, such as an immersion heater, is determined by the voltage applied and the resistance of the element, following the relation P = V²/R. It is fundamental in determining how changes in voltage affect the heating rate, since power is directly related to the rate at which electrical energy is converted into heat.

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