How do you calculate the total resistance of resistors in series and parallel circuits?

Resistors in Series:

When resistors are connected in series, they are arranged in a single line, and the current flowing through each resistor is the same. To calculate the total resistance (R_total) of resistors in series, you simply need to sum up the individual resistances (R1, R2, R3, ..., Rn):

R_total = R1 + R2 + R3 + ... + Rn

For example, if you have three resistors in series with values of 10 ohms, 20 ohms, and 30 ohms, the total resistance would be:

R_total = 10 ohms + 20 ohms + 30 ohms = 60 ohms

Resistors in Parallel:

When resistors are connected in parallel, they are arranged in multiple branches, and the voltage across each resistor is the same. To calculate the total resistance (R_total) of resistors in parallel, you use the following formula:

1/R_total = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Once you have the sum of the reciprocals of the individual resistances, take the reciprocal of that sum to get the total resistance:

R_total = 1 / (1/R1 + 1/R2 + 1/R3 + ... + 1/Rn)

For example, if you have three resistors in parallel with values of 10 ohms, 20 ohms, and 30 ohms, the total resistance would be:

R_total = 1 / (1/10 ohms + 1/20 ohms + 1/30 ohms)

R_total = 1 / (0.1 + 0.05 + 0.0333) ≈ 5.4545 ohms

Remember that in parallel, the total resistance will always be smaller than the smallest individual resistor because having multiple paths for current flow reduces the overall resistance.

In summary, for resistors in series, add up the resistances to get the total resistance, and for resistors in parallel, use the reciprocal of the sum of the reciprocals of the individual resistances to get the total resistance.