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 dangerously large total current by "opening" to stop the current at a specified safe value. A 1650 -W toaster, a 1090 -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 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

Circuit Breaker Operation

Circuit breakers are safety devices designed to protect circuits from excessive current that might cause damage or fire. They automatically interrupt the current flow when the total current exceeds a specified threshold, ensuring that connected devices and wiring remain safe from overcurrent conditions.

Ohm's Law

Ohm's Law states that the voltage across a resistor is proportional to the current flowing through it, with the proportionality constant being the resistance. This fundamental relationship, expressed as V = IR, is used to analyze circuits and determine parameters such as current, voltage drops, and resistance values.

Electrical Power

Electrical power in a circuit is defined as the rate at which energy is consumed or converted, and is given by the relation P = IV. Power can also be expressed in terms of voltage and resistance using the formulas P = V²/R or P = I²R, which help in calculating the resistance of devices from their power ratings.

Parallel Circuits

In parallel circuits, all components are connected across the same voltage source, and the total current supplied by the source is the sum of the currents through each component. This configuration allows for the independent operation of devices, where each branch experiences the full supply voltage.

Equivalent Resistance in Parallel Circuits

The equivalent resistance of components connected in parallel is found using the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn, where Req is always less than the smallest individual resistance. This concept is crucial for determining the overall resistance of a circuit with multiple branches.

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