A resistor is an electronic component that is used to resist or oppose the flow of electric current in a circuit. It is a passive component, which means that it does not require any external power source to function.

Resistors are typically made of materials such as carbon, metal, or wire-wound materials. They come in a variety of shapes and sizes, and are marked with a color code or numerical value that indicates their resistance. The unit of resistance is ohms, symbolized by the Greek letter omega (Ω).

Resistors are commonly used in electronic circuits to control the flow of current, limit the amount of current that flows through a circuit, and provide a specific voltage drop. They can also be used to divide voltage, generate heat, and perform other functions.

Overall, resistors are essential components in electronics and electrical engineering, and are used in a wide range of applications in devices such as computers, televisions, radios, and more.

**Series and parallel resistors**

Resistors can be connected in two ways – in series and in parallel.

In a series connection, the resistors are connected end to end such that the current flows through each resistor in turn. The total resistance of the series connection is equal to the sum of the individual resistances. In other words, the total resistance is greater than the resistance of any single resistor. The current through each resistor is the same, but the voltage across each resistor is different, with the voltage dropping across each resistor in proportion to its resistance.

When resistors are connected in series, the total resistance (R_total) is equal to the sum of the individual resistances (R1, R2, R3, etc.):

R_total = R1 + R2 + R3 + …

For example, if two resistors of 10 ohms and 20 ohms are connected in series, the total resistance would be:

R_total = 10 ohms + 20 ohms = 30 ohms

In a parallel connection, the resistors are connected side by side such that the current splits and flows through each resistor simultaneously. The total resistance of the parallel connection is less than the resistance of any single resistor. In other words, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. The voltage across each resistor is the same, but the current through each resistor is different, with the current through each resistor proportional to its conductance (the reciprocal of its resistance).

When resistors are connected in parallel, the reciprocal of the total resistance (1/R_total) is equal to the sum of the reciprocals of the individual resistances:

1/R_total = 1/R1 + 1/R2 + 1/R3 + …

The total resistance is then calculated as the reciprocal of this sum:

R_total = 1 / (1/R1 + 1/R2 + 1/R3 + …)

For example, if two resistors of 10 ohms and 20 ohms are connected in parallel, the total resistance would be:

1/R_total = 1/10 ohms + 1/20 ohms = 0.1 + 0.05 = 0.15 R_total = 1 / 0.15 = 6.67 ohms

Series and parallel resistor connections have different effects on the overall resistance and current of the circuit. By understanding how to calculate the total resistance and current in each type of connection, one can design circuits with the desired electrical characteristics.