Resisitors in Series

Overview

Most circuits have more than one component, called a resistor, that limits the flow of charge in the circuit. A measure of this limit on charge flow is called resistance. The simplest combinations of resistors are the series and parallel connections. The total resistance of a combination of resistors depends on both their individual values and how they are connected.

Resistors in Series

Resistors are in series whenever the flow of charge, or the current, must flow through components sequentially .

Resistors in Series

These four resistors are connected in series because if a current was applied at one end, it would flow through each resistor sequentially to the end.

shows resistors in series connected to a voltage source. The total resistance in the circuit is equal to the sum of the individual resistances, since the current has to pass through each resistor in sequence through the circuit.

Resistors connected in a series circuit

Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).

Using Ohm's Law to Calculate Voltage Changes in Resistors in Series

According to Ohm's law, the voltage drop, V, across a resistor when a current flows through it is calculated by using the equation V=IR, where I is current in amps (A) and R is the resistance in ohms (Ω).

So the voltage drop across R₁ is V₁=IR₁, across R₂ is V₂=IR₂, and across R₃ is V₃=IR₃. The sum of the voltages would equal: V=V₁+V₂+V₃, based on the conservation of energy and charge. If we substitute the values for individual voltages, we get:

$V=IR_1 + IR_2 + IR_3$

or

$V = I(R_1+R_2+R_3)$

This implies that the total resistance in a series is equal to the sum of the individual resistances. Therefore, for every circuit with N number of resistors connected in series:

$RN (series) = R_1 + R_2 + R_3 + ... + R_N.$

Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up.

Since voltage and resistance have an inverse relationship, individual resistors in series do not get the total source voltage, but divide it. This is indicated in an example of when two light bulbs are connected together in a series circuit with a battery. In a simple circuit consisting of one 1.5V battery and one light bulb, the light bulb would have a voltage drop of 1.5V across it. If two lightbulbs were connected in series with the same battery, however, they would each have 1.5V/2, or 0.75V drop across them. This would be evident in the brightness of the lights: each of the two light bulbs connected in series would be half as dim as the single light bulb. Therefore, resistors connected in series use up the same amount of energy as a single resistor, but that energy is divided up between the resistors depending on their resistances.