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Resistors are one of the most basic and common components in electrical circuits. They are used to limit the current flow and create voltage drops in various applications. In this article, we will review the concepts of resistors in series and parallel connections, and provide some practice problems for you to test your understanding. You can also download a PDF file with the solutions at the end of the article.

## Resistors in Series

Resistors are said to be in series whenever the current flows through the resistors sequentially. Consider the following circuit diagram, which shows three resistors in series with an applied voltage equal to Vab.

Since there is only one path for the charges to flow through, the current is the same through each resistor. The equivalent resistance of a set of resistors in a series connection is equal to the algebraic sum of the individual resistances.

Req = R1 + R2 + R3

The current through the circuit depends on the voltage supplied by the voltage source and the resistance of the resistors. For each resistor, a potential drop occurs that is equal to the loss of electric potential energy as a current travels through each resistor. According to Ohms law, the potential drop V across a resistor when a current flows through it is calculated using the equation V = IR, where I is the current in amps (A) and R is the resistance in ohms (Ω).

V1 = I R1

V2 = I R2

V3 = I R3

The sum of the potential drops across each resistor is equal to the total voltage supplied by the source.

Vab = V1 + V2 + V3

## Resistors in Parallel

Resistors are said to be in parallel whenever they are connected across the same pair of terminals. Consider the following circuit diagram, which shows three resistors in parallel with an applied voltage equal to Va.

In this case, there are multiple paths for the charges to flow through, and the current splits among them. The equivalent resistance of a set of resistors in a parallel connection is given by the reciprocal of the sum of the reciprocals of the individual resistances.

\frac1R_eq = \frac1R_1 + \frac1R_2 + \frac1R_3

The voltage across each resistor is equal to the voltage supplied by the source, since they are connected across the same terminals.

Va = V1 = V2 = V3

The current through each resistor is inversely proportional to its resistance, according to Ohms law.

I1 = \fracV_aR_1

I2 = \fracV_aR_2

I3 = \fracV_aR_3

The sum of the currents through each resistor is equal to the total current supplied by the source.

I = I1+ I2+ I3

## - [Ohms Law III -- Resistors in Series and Parallel] - [10.3: Resistors in Series and Parallel - Physics LibreTexts] - [Series and parallel resistors (practice) Khan Academy] Practice Problems

Here are some practice problems for you to apply the concepts of resistors in series and parallel. You can use a calculator and a paper to solve them. The answers are given in the PDF file that you can download below.

• What is the equivalent resistance of the following circuit?

• What is the current through each resistor in the following circuit?

• What is the voltage across each resistor in the following circuit?

• What is the power dissipated by each resistor in the following circuit?