Calculating Total Resistance: Series vs Parallel Resistors
Students often struggle to understand the difference between series and parallel resistor connections. Don’t worry, this is a core concept, and once you grasp it, you’ll find it much easier to understand how circuits behave in real-world situations. Electric current takes different paths as per the connections of resistances and their values.
When multiple resistors are used in a circuit, knowing how to calculate the total resistance is crucial to ensure the circuit works correctly and safely. The method for calculating total resistance depends on how the resistors are connected – in series, in parallel, or in a series and parallel combination.
Resistors in Series
When resistors are connected end-to-end, they are in series. Think of it like a single path where electricity has to flow through each resistor one after another.
Key Point: In a series connection, the total resistance is simply the sum of the individual resistances.
Rtotal = R1 + R2 + ……. + Rn
Insight: The total resistance increases when more resistors are added in series, as the current must pass through each one.
Resistors in Parallel
When resistors are connected side-by-side, they are arranged in parallel. In this configuration, the current splits and flows through multiple paths simultaneously.
Key Point: In a parallel connection, the total resistance decreases because the current has more paths to flow through.
1/Rtotal = 1/R1+1/R2+ ……… + 1/Rn
Insight: The total resistance is always less than the smallest resistor in the parallel combination.
Refer to the Ausinet Parallel Resistance calculator to calculate the total resistance in a parallel circuit.
Series-Parallel Combination Circuits
Most real-world circuits don’t use resistors just in series or just parallel; they’re a combination of both.
How to Calculate Combination Circuits:
Step 1: Identify and simplify the parallel sections first using the parallel formula.
Step 2: Add the result to any series resistors using the series formula.
Step 3: Continue simplifying the circuit until you reduce it to a single equivalent resistance.
Example – Find the total resistance of the circuit with reference to point AB
Using the Ausinet calculator, find out the equivalent resistance of the parallel combination.
Add the result to any series resistors using the series formula.
Total resistance = resistance of parallel combination + series resistance
= 1393.33 + 12000
= 13393.33 ohm