How do you calculate the total resistance of resistors in series and in parallel?
1 Answer
To calculate the total resistance of resistors in series and in parallel, you can use the following formulas:
Resistors in Series:
When resistors are connected in series, their resistances add up to give the total resistance.
Total Resistance (Rs) = R1 + R2 + R3 + ... + Rn
Where:
Rs is the total resistance of the resistors in series,
R1, R2, R3, ..., Rn are the individual resistances of each resistor.
Example:
If you have three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms connected in series, the total resistance would be:
Rs = 10 ohms + 20 ohms + 30 ohms = 60 ohms.
Resistors in Parallel:
When resistors are connected in parallel, the reciprocal of their resistances adds up to give the inverse of the total resistance. You then take the reciprocal of that sum to get the total resistance.
Total Resistance (Rp) = 1 / (1/R1 + 1/R2 + 1/R3 + ... + 1/Rn)
Where:
Rp is the total resistance of the resistors in parallel,
R1, R2, R3, ..., Rn are the individual resistances of each resistor.
Example:
If you have three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms connected in parallel, the total resistance would be:
Rp = 1 / (1/10 ohms + 1/20 ohms + 1/30 ohms)
Rp = 1 / (0.1 + 0.05 + 0.0333)
Rp = 1 / 0.1833
Rp ≈ 5.45 ohms.
Remember that resistors in series increase the total resistance, while resistors in parallel decrease it. These formulas apply not only to three resistors but to any number of resistors connected in series or parallel.
Resistors in Series:
When resistors are connected in series, their resistances add up to give the total resistance.
Total Resistance (Rs) = R1 + R2 + R3 + ... + Rn
Where:
Rs is the total resistance of the resistors in series,
R1, R2, R3, ..., Rn are the individual resistances of each resistor.
Example:
If you have three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms connected in series, the total resistance would be:
Rs = 10 ohms + 20 ohms + 30 ohms = 60 ohms.
Resistors in Parallel:
When resistors are connected in parallel, the reciprocal of their resistances adds up to give the inverse of the total resistance. You then take the reciprocal of that sum to get the total resistance.
Total Resistance (Rp) = 1 / (1/R1 + 1/R2 + 1/R3 + ... + 1/Rn)
Where:
Rp is the total resistance of the resistors in parallel,
R1, R2, R3, ..., Rn are the individual resistances of each resistor.
Example:
If you have three resistors with resistances of 10 ohms, 20 ohms, and 30 ohms connected in parallel, the total resistance would be:
Rp = 1 / (1/10 ohms + 1/20 ohms + 1/30 ohms)
Rp = 1 / (0.1 + 0.05 + 0.0333)
Rp = 1 / 0.1833
Rp ≈ 5.45 ohms.
Remember that resistors in series increase the total resistance, while resistors in parallel decrease it. These formulas apply not only to three resistors but to any number of resistors connected in series or parallel.