Three 9.0-Ωresistors are connected in series with a 12-V battery. Find (a) the equivalent resist

step 1 It's been said that 3 9 -oom resistances are connected in series. So first we'll make a circuit

Three 9.0-Ωresistors are connected in series with a 12-V...

Three $9.0-\Omega$ resistors are connected in series with a $12-\mathrm{V}$ battery. Find (a) the equivalent resistance of the circuit and (b) the current in each resistor. (c) Repeat for the case in which all three resistors are connected in parallel across the battery.

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Key Concepts

Series Resistor Connection

In a series resistor connection, all resistors are connected one after the other such that the same current flows through each resistor. The overall or equivalent resistance is simply the sum of the individual resistances. This concept is important for analyzing circuits where the current remains constant and the voltage drop is divided among the resistors.

Parallel Resistor Connection

In a parallel resistor connection, each resistor is connected directly across the same two nodes, so they all experience the same voltage. The equivalent resistance of resistors in parallel is determined by the reciprocal of the sum of the reciprocals of their resistances. This configuration results in a lower equivalent resistance than any individual resistor and causes the total current to divide among the parallel branches.

Ohm's Law

Ohm's Law is a fundamental relationship in electrical circuits, linking voltage (V), current (I), and resistance (R) by the equation I = V/R. This law is essential for determining how current flows through components and for calculating voltage drops across resistors in both series and parallel circuits.

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