is no detour path for the current to follow.
This phenomenon is explored in more detail in Example 1. Two light bulbs are wired in
series, similar to old-fashioned holiday lights. The filament of each light bulb is part of
the circuit. When a light bulb burns out, its filament breaks, and there is no path for
current through that bulb. The example problem asks what happens to the second light
bulb in a series circuit if the first bulb burns out.
Current same at all points
If light bulb A burns out, will light
bulb B remain lit?
Noí a break in a series circuit causes
all current to stop
27.6 - Resistors in series
To calculate the equivalent resistance of
resistors in series: Add each resistor’s
resistance.
Analyzing circuits with multiple components can be complex. The task can sometimes
be simplified by treating several components of the same type as if they were one. You
can simplify a circuit by calculating what is called the “equivalent resistance” or
“equivalent capacitance” of multiple resistors or capacitors. You can then treat the
components as one, using their equivalent resistance or equivalent capacitance.
Our first case for doing this is resistors in series. Once we determine their equivalent
resistance, we can treat them as though they were one component, and determine how
much current flows through the circuit in Example 1. In the case of resistors wired in
series, the equivalent resistance is the sum of the resistances. We show this in
Equation 1.
Consider the circuit shown in Example 1 that contains two resistors in series. The
question asks for the amount of current in this circuit. You can determine the current
using Ohm’s law, ǻV= IR, but what should you use for R?
First, determine the series circuit’s equivalent resistance by summing the individual
resistances. The 6 ȍ resistor plus the 4 ȍ resistor equals an equivalent resistance of
10 ȍ. The circuit in the example has a 20-volt battery. Since the two resistors create an
equivalent resistance of 10 ȍ, you can use Ohm’s law to calculate the current through
them. It equals 20 V divided by 10 ȍ, or 2 A.
Derivation. Why can resistances in series be added? We now derive the series rule for
resistors, for n resistors in series.
Variables
Strategy
- Find the total potential difference across all the resistors combined.
- Use Ohm’s law to rewrite potential difference in terms of current and resistance.
An algebraic simplification gives the series rule for resistors.
Resistors in series
Requiv = R 1 + R 2 +...+ Rn
Equivalent resistance = sum of
individual resistances
What is the equivalent resistance
of the resistors and what is the
current?
Requiv = R 1 + R 2
Requiv = 6 ȍ + 4 ȍ = 10 ȍ
potential difference across all resistors ǻVtotal
potential difference across ith resistor ǻVi
current through circuit Icurrent through ith resistor Ii
equivalent resistance of circuit Requivresistance of ith resistor Ri