A short circuit in a 120 -V appliance cord has a 0.500-Ωresistance. Calculate the temperature ri

step 1 In this question we have a short circuit scenario with a 120 volts source and we have the applia

A short circuit in a 120 -V appliance cord has a...

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 $0.0500 \mathrm{s}$ for a circuit breaker to interrupt the current. Is this likely to be damaging?

Key Concepts

Circuit Protection and Response Time

Circuit protection devices, such as circuit breakers, are designed to interrupt current flow quickly when it exceeds safe levels. The time interval between the onset of a short circuit and the activation of a breaker is vital to determining how much energy is dissipated as heat, affecting whether the transient temperature rise might cause damage or compromise component integrity.

Short Circuit

A short circuit occurs when an unintended low resistance connection is made between two points in an electrical circuit, resulting in a large amount of current flow. This sudden surge in current can generate significant heat rapidly, posing risks to both the electrical system and surrounding materials, which is why understanding energy dissipation is crucial.

Specific Heat Capacity

Specific heat capacity is a property of a material that indicates how much energy is needed to raise the temperature of a unit mass of the substance by one degree Celsius. The relationship Q = mc?T links the heat energy absorbed (Q) to the mass (m), specific heat capacity (c), and the resulting temperature change (?T). This principle allows the assessment of temperature increase due to the absorbed energy from Joule heating.

Joule Heating

Joule heating, also known as resistive heating, is the process by which the passage of an electric current through a conductor produces heat. The power dissipated as heat can be calculated using the formula P = I^2R, and the total energy generated over a time period is given by E = I^2Rt. This concept is critical for understanding how electrical energy can convert into thermal energy in a circuit fault.

Ohm's Law

Ohm’s Law defines the relationship between voltage, current, and resistance in an electrical circuit. It states that V = IR, which allows one to calculate the current flowing through a resistance when the voltage is known. This concept is foundational for analyzing electrical circuits and determining how much current will pass through a component like a short-circuited cord.

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