How do you calculate the equivalent resistance of resistors in series and parallel configurations?

Resistors in Series:

When resistors are connected in series, they form a single path for the current to flow. The total resistance (equivalent resistance) can be calculated by simply adding up the individual resistances.

For n resistors in series, the formula is:

Equivalent Resistance (Rs) = R1 + R2 + R3 + ... + Rn

where R1, R2, R3, ..., Rn are the individual resistances in series.

Resistors in Parallel:

When resistors are connected in parallel, they provide multiple paths for the current to flow. The reciprocal of the total resistance (equivalent resistance) is equal to the sum of the reciprocals of the individual resistances.

For n resistors in parallel, the formula is:

1 / Equivalent Resistance (Rp) = 1 / R1 + 1 / R2 + 1 / R3 + ... + 1 / Rn

To get the equivalent resistance (Rp), you take the reciprocal of the sum of the reciprocals:

Equivalent Resistance (Rp) = 1 / (1 / R1 + 1 / R2 + 1 / R3 + ... + 1 / Rn)

where R1, R2, R3, ..., Rn are the individual resistances in parallel.

In practice, for two resistors in parallel (R1 and R2), a simplified formula can be used:

Equivalent Resistance (Rp) = (R1 * R2) / (R1 + R2)

This equation allows you to calculate the equivalent resistance when you have two resistors in parallel.

Keep in mind that the unit of resistance is the ohm (Ω). Always ensure that the individual resistances are in the same unit before performing the calculations. Additionally, for more complex configurations involving both series and parallel resistors, you may need to simplify the circuit step by step until you can find the overall equivalent resistance.