The total current delivered to a number of devices connected...

The total current delivered to a number of devices connected in parallel is the sum of the individual currents in each device. Circuit breakers are resettable automatic switches that protect against a danCircuit gerously large total current by "opening" to stop the current at a specified safe value. A $1650-\mathrm{W}$ toaster, a $1090-\mathrm{W}$ iron, and a 1250-W microwave oven are turned on in a kitchen. As the drawing shows, they are all connected through a 20 -A circuit breaker (which has negligible resistance) to an ac voltage of $120 \mathrm{~V}$. (a) Find the equivalent resistance of the three devices. (b) Obtain the total current delivered by the source and determine whether the breaker will "open" to prevent an accident.

The total current delivered to a number of devices connected in parallel is the sum of the individual currents in each device. Circuit breakers are resettable automatic switches that protect against a danCircuit
gerously large total current by "opening" to stop the current at a specified safe value. A $1650-\mathrm{W}$ toaster, a $1090-\mathrm{W}$ iron, and a 1250-W microwave oven are turned on in a kitchen. As the drawing shows, they are all connected through a 20 -A circuit breaker (which has negligible resistance) to an ac voltage of $120 \mathrm{~V}$.
(a) Find the equivalent resistance of the three devices. (b) Obtain the total current delivered by the source and determine whether the breaker will "open" to prevent an accident.

Key Concepts

Power and Resistance Relationship

The relationship between power, voltage, and resistance is given by the formula P = V²/R, which allows the conversion of a device’s power rating into an effective resistance value. This concept is crucial when analyzing circuits to determine how each device contributes to the overall resistance and current draw.

Parallel Circuits

A parallel circuit feature implies that all connected components share the same voltage across them, while the overall current is divided among the parallel branches. This configuration plays a critical role in analyzing how current adds up from multiple devices connected to the same source.

Equivalent Resistance in Parallel Circuits

When resistive components are connected in parallel, the total resistance of the circuit is found by taking the reciprocal of the sum of the reciprocals of each individual resistance. This computation simplifies the analysis of circuits by reducing a network of resistors to a single equivalent resistance.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits stating that the voltage across a resistor is directly proportional to the current flowing through it, represented by the equation V = IR. This relationship is essential for determining unknown values within a circuit once two parameters are known.

Circuit Breakers as Protective Devices

Circuit breakers are safety devices that automatically interrupt current flow when it exceeds a pre-set level, protecting circuits from damage due to overcurrent. They are critical in preventing potential hazards such as overheating and electrical fires by breaking the circuit before dangerous conditions arise.

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