Integrated Concepts A short circuit in a 120 -V appliance...

Integrated Concepts A short circuit in a 120 -V appliance cord has a $0.500-\Omega$ resistance. Calculate the temperature rise of the 2.00 g of surrounding materials, assuming their specific heat capacity is 0.200 $\mathrm{cal} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ and that it takes 0.0500 s for a circuit breaker to interrupt the current. Is this likely to be damaging?

Integrated Concepts
A short circuit in a 120 -V appliance cord has a $0.500-\Omega$ resistance. Calculate the temperature rise of the 2.00 g of surrounding materials, assuming their specific heat capacity is 0.200 $\mathrm{cal} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ and that it takes 0.0500 s for a circuit breaker to interrupt the current. Is this likely to be damaging?

Key Concepts

Ohm’s Law and Electrical Resistance

Understanding the relationship between voltage, current, and resistance is fundamental in electric circuits. Ohm’s Law (V = IR) allows us to determine the current flowing through a device or circuit element when the voltage and resistance are known. In the context of this problem, the resistance of the short circuit is key to calculating the amount of current, which directly influences the power dissipation through heating.

Joule Heating (Power Dissipation)

When current flows through a resistor, electrical energy is converted into thermal energy due to the resistance’s opposition to current flow—this is known as Joule heating. The power dissipated can be calculated using the formula P = V^2/R. This concept is crucial for understanding how an electrical fault, like a short circuit, can lead to rapid increases in temperature.

Energy Transfer in a Given Time Interval

The energy converted into heat over time can be determined by multiplying the power (rate of energy conversion) by the time the current flows. This time-dependent aspect is significant because it defines the duration over which the short circuit heats the surrounding material, influencing the total energy absorbed.

Specific Heat Capacity and Temperature Change

Specific heat capacity (the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius) is used to calculate the temperature rise when the absorbed energy is transferred to a material. The relationship ?T = Q/(m·c) connects the energy absorbed (Q) to the mass (m) and the specific heat capacity (c) of the material, providing a method to assess potential thermal damage.

Circuit Breaker Response Time

The circuit breaker’s interruption time is critical in limiting the energy delivered during a short circuit. This concept ties into safety mechanisms in electrical systems, as shorter interruption times reduce the amount of energy that can be dissipated into the system, potentially preventing extensive thermal damage.

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