Learning Goal:

To practice Problem$-$Solving Strategy $19\mathrm{.}1$ Resistors in series and in parallel.

Six equal resistors are connected as shown. $($Figure $1)$ If the resistance of a single resistor is $6\mathrm{.}00,$ find the equivalent resistance of the entire circuit, ReqReq.

Figure

$1$ of $1$

Problem$-$Solving Strategy $19\mathrm{.}1$ Resistors in series and in parallel

SET UP

It helps to remember that when resistors are connected in series, the total potential difference across the combination is the sum of the individual potential differences. When resistors are connected in parallel, the potential difference is the same for every resistor and is equal to the potential difference across the parallel combination.

Also, keep in mind the analogous statements for current: When resistors are connected in series, the current is the same through every resistor and is equal to the current through the series combination. When resistors are connected in parallel, the total current through the combination is equal to the sum of currents through the individual resistors.

SOLVE

We can often consider complicated networks to be combinations of series and parallel arrangements. We then replace each simple series or parallel combination by its equivalent resistance.

REFLECT

The rule for combining resistors in parallel follows directly from the principle of conservation of charge. The rule for combining resistors in series results from a fundamental principle about work: When a particle moves along a path, the total work done on it is the sum of the quantities of work done during the individual segments of the path.

SET UP

Before writing any equations, organize your information and draw appropriate diagrams.

Part A

Part complete

Are resistors A and B connected in series or in parallel?

seriesparallel

SubmitPrevious$$Answers

Correct

Part B

Part complete

How many parallel branches are there in the circuit?

Express your answer numerically as an integer.

$2$

SubmitPrevious$$Answers

Correct

SOLVE

Now that you$$ve set up the problem, choose appropriate equations and solve for your unknowns.

Part C

What is the equivalent resistance ReqReq of the entire circuit?

Express your answer in ohms to three significant figures.

View Available Hint$($s$)$for Part C

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

ReqReq $=$

$2$

$$