A 6.00-V battery supplies current to the circuit shown in...

A $6.00-\mathrm{V}$ battery supplies current to the circuit shown in Figure P28.14. When the double-throw switch S is open, as shown in the figure, the current in the battery is $1.00 \mathrm{mA}$ When the switch is closed in position $1,$ the current in the battery is $1.20 \mathrm{mA}$. When the switch is closed in position 2 the current in the battery is 2.00 mA. Find the resistances $R_{1}, R_{2},$ and $R_{3}$ FIGURE CANT COPY

Key Concepts

Kirchhoff's Laws

Kirchhoff's Voltage and Current Laws are essential tools for analyzing circuits. Kirchhoff's Voltage Law states that the sum of all voltage drops in a closed loop equals the supplied voltage, while Kirchhoff's Current Law states that the total current entering a junction equals the total current leaving it. These laws help in setting up the equations needed to solve for unknown resistances.

Equivalent Resistance

The concept of equivalent resistance refers to the single resistance that can replace a combination of resistors without changing the overall current drawn from a voltage source. Calculating equivalent resistance is a key step when dealing with circuits that have multiple resistive paths, particularly when switches alter the circuit configuration.

Switching Circuit Configurations

Switching circuit configurations involves changing the connections within a circuit using switches to alter paths and control the flow of current. Understanding how closing or opening a switch affects the circuit's overall resistance and current distribution is essential for analyzing circuits with variable connections.

Ohm's Law

Ohm's Law is a fundamental principle in electric circuits, stating that the voltage across a resistor is directly proportional to the current flowing through it, with the resistance being the constant of proportionality. This relationship (V = IR) is essential for analyzing how voltage, current, and resistance interact in any circuit.

Series and Parallel Circuits

Understanding series and parallel circuits is crucial when analyzing complex networks. In series circuits, resistances add directly, while in parallel circuits, the total resistance is found using the reciprocal formula. Recognizing these configurations allows for the determination of equivalent resistances, simplifying circuit analysis.

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