When two resistors are wired in series with a 12 V battery, the current through the battery is 0

step 1 Hi, suppose the two unknown resistors are having the values of R1 and R2. When these two resisto

When two resistors are wired in series with a 12 V battery,...

When two resistors are wired in series with a $12 \mathrm{V}$ battery, the current through the battery is 0.30 A. When they are wired in parallel with the same battery, the current is $1.6 \mathrm{A}$. What are the values of the two resistors?

Key Concepts

Equivalent Resistance

Equivalent resistance is the total resistance that can replace a combination of series or parallel resistors in a circuit without altering the current or voltage. In series circuits, equivalent resistance is the sum of all resistances, while in parallel circuits, it is calculated by taking the reciprocal of the sum of the reciprocals of each individual resistance. This concept simplifies the analysis of complex circuits by reducing them to a single resistance value.

Parallel Circuit

A parallel circuit is a configuration where electrical components are connected across common points, forming multiple paths for the current to flow. In parallel circuits, the voltage across each component is the same, but the total current is the sum of the currents through each branch. This concept is important for analyzing how resistance, current, and voltage distribute in a network of components.

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. This relationship, expressed as V = IR, is crucial for analyzing how voltage, current, and resistance interact in any circuit configuration.

Series Circuit

A series circuit is a configuration in which electrical components are connected end-to-end in a single path for the current to flow. In such circuits, the same current flows through all components, and the total resistance is the sum of individual resistances. Understanding series circuits is essential when calculating voltage drops and the overall resistance in the circuit.

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