Conceptual Physics

whether the resulting equivalent resistance is in series or parallel with other resistors. Continue this process until the circuit cannot be

simplified any further.

Physics principles and equations

Resistors are wired in series if there is only a single path for current to flow through them.

Branches are wired in parallel if the potential difference across them is the same.

Step 1

We start by checking for resistors in series. As the circuit is depicted above, none of these resistors are wired in series. The current running

through any of the three resistors branches before reaching any of the other resistors.

Step 2

Next we check for parallel resistors. The resistors R 2 and R 3 are wired in parallel.

Step 3

Now, we reexamine the circuit having made a parallel combination out of R 2 and R 3. The resistor R 1 is in series with the equivalent resistance

of the R 2 R 3 combination. This may be tricky to see, but applying the tests for series wiring confirms it. The same current flows through R 1 as

flows through the equivalent combination of R 2 and R 3. Another way of saying this is that the sum of the currents going to R 2 and R 3 is equal to

the current through R 1.

(Note: It is possible to create circuits that are irreducible, in which the components are neither in parallel nor in series. If you think you have

simplified a circuit as much as you can, you may be right.)

27.14 - Gotchas

Components in series must have the same potential difference across them. No, they have the same amount of current flowing through them.

The potential difference across components in parallel is the same. Yes.

27.15 - Summary

An electric circuit is a set of electric components such as batteries, capacitors and

resistors that are connected directly or through wires.

Current will only flow through a circuit that is closed, which means that it makes a

loop. To cause current to flow continuously through a circuit, a source of emf, Ǜ,

such as a battery, must be present.

One basic type of circuit wiring is series wiring. Two circuit components are said to

be in series when current must go through both components: there is only one

possible path. The same amount of current flows through both components, and the

sum of the potential differences across the components is the net potential

difference across the combination.

Resistances in series add to give the equivalent resistance of a combination of

resistors.

The other basic type of wiring is parallel wiring. Components are connected so that they have the same potential difference across them, but

may have different currents through them.

The sum of the reciprocals of resistances wired in parallel equals the reciprocal of the equivalent resistance of a combination of resistors.

Resistors in series

Requiv = R 1 + R 2 +...+ Rn

Resistors in parallel

(^498) Copyright 2000-2007 Kinetic Books Co. Chapter 27