Series & Parallel Resistance
Calculate total resistance for resistors connected in series or parallel. Add up to 10 resistors.
How series and parallel circuits differ
Frequently asked questions
Why is parallel resistance always less than the smallest resistor?
In a parallel circuit, adding more resistors provides additional paths for current to flow. More current paths means less overall opposition to current, so total resistance decreases. Mathematically, 1/R_total is always greater than any individual 1/R_n, so R_total is always less than any individual R_n.
What is the formula for two resistors in parallel?
For exactly two resistors: R_total = (R1 × R2) / (R1 + R2). This is the "product over sum" formula. For example, 4Ω and 12Ω in parallel: R_total = (4 × 12) / (4 + 12) = 48/16 = 3Ω.
Do identical resistors in parallel give half the resistance?
Yes. Two identical resistors R in parallel give R/2. Three give R/3. n identical resistors R in parallel give R/n. This is because 1/R_total = n/R, so R_total = R/n.
How do home electrical circuits use parallel connections?
Household electrical circuits connect appliances in parallel so each device gets the same voltage (230V in India) and can be switched independently. If they were in series, switching off one device would break the circuit for all others.
What happens to total resistance when you add a resistor in parallel?
Adding any resistor in parallel always decreases the total resistance, even if the added resistor is very large. This is because any finite resistance provides some additional current path. Adding a very large resistor has minimal effect, but the total will always be slightly lower.