Resistors in series and parallel
Resistors in series
When resistors are connected in series, the current through each resistor is the same. In other words, the current is the same at all points in a series circuit.
When resistors are connected in series, the total voltage (or potential difference) across all the resistors is equal to the sum of the voltages across each resistor.
In other words, the voltages around the circuit add up to the voltage of the supply.
The total resistance of a number of resistors in series is equal to the sum of all the individual resistances.
In this circuit the following applies.
I1 = I2 = I3
VT = V1 + V2 + V3
and, RT = R1 + R2 + R3
Resistors in parallel
When resistors are connected in parallel, the supply current is equal to the sum of the currents through each resistor. The currents in the branches of a parallel circuit add up to the supply current.
When resistors are connected in parallel, they have the same potential difference across them. Any components in parallel have the same potential difference across them.
In order to calculate the total resistance of two resistors connected in parallel, this equation is used.
\(\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}\)
To calculate the total resistance of three resistors connected in parallel, we add a third resistor to the equation (and so on).
\(\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}+\frac{1}{R}_{3}\)
Question
Calculate the resistance of this parallel combination.
\(\frac{1}{R}=\frac{1}{R}_{1}+\frac{1}{R}_{2}+\frac{1}{R}_{3}\)
\(\frac{1}{R}=\frac{1}{3}+\frac{1}{6}+\frac{1}{9}\)
R = 1.64 Ω