Take ℰ=12 V and R1=270 Ωin Fig. 25.4 . (a) What's the...

Take $\mathcal{E}=12 \mathrm{V}$ and $R_{1}=270 \Omega$ in Fig. $25.4 .$ (a) What's the resistance $R_{2}$ if there's $4.5 \mathrm{V}$ across it? (b) What will be the power dissipation in $R_{2} ?$

Key Concepts

Voltage Divider

This concept refers to the way voltage is apportioned among resistors connected in series. In a voltage divider, the voltage across any resistor is proportional to its resistance relative to the total series resistance. This principle is widely used to obtain a desired voltage from a higher voltage source by carefully selecting resistor values.

Ohm's Law

Ohm's Law is the fundamental relationship between voltage, current, and resistance in an electrical circuit, expressed as V = I × R. It is essential for calculating unknown quantities in circuits, including the voltage drop across components, the current flowing through them, or their resistance.

Series Circuits

In series circuits, the same current flows through all components because they are connected end-to-end. The total resistance is the sum of the individual resistances, and the voltage across the circuit is divided among the components according to their resistances. Understanding series circuits is crucial for analyzing how voltage and current are distributed in a circuit.

Power Dissipation in Resistive Circuits

This concept involves calculating the electrical power converted into heat in a resistor. The power dissipated can be expressed by the formulas P = V^2 / R or P = I^2 × R. It is an important consideration in circuit design to ensure components do not overheat and that the circuit operates efficiently.

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