18.1 Resistance (Page 33/2)

Siyavula textbooks: grade 11 Page 1 / 2

Resistance

In Grade 10, you learnt about resistors and were introduced to circuits where resistors were connected in series and circuits where resistors were connected in parallel. In a series circuit there is one path for the current to flow through. In a parallel circuit there are multiple paths for the current to flow through.

Equivalent resistance

When there is more than one resistor in a circuit, we are usually able to calculate the total combined resitance of all the resistors. The resistance of the single resistor is known as equivalent resistance .

Equivalent series resistance

Consider a circuit consisting of three resistors and a single cell connected in series.

The first principle to understand about series circuits is that the amount of current is the same through any component in the circuit. This is because there is only one path for electrons to flow in a series circuit. From the way that the battery is connected, we can tell which direction the current will flow. We know that current flows from positive to negative, by convention. Current in this circuit will flow in a clockwise direction, from point A to B to C to D and back to A.

So, how do we use this knowledge to calculate the total resistance in the circuit?

We know that in a series circuit the current has to be the same in all components. So we can write:

I = I_{1} = I_{2} = I_{3}

We also know that total voltage of the circuit has to be equal to the sum of the voltages over all three resistors. So we can write:

V = V_{1} + V_{2} + V_{3}

Finally, we know that Ohm's Law has to apply for each resistor individually, which gives us:

\begin{matrix} V_{1} & = & I_{1} \cdot R_{1} \\ V_{2} & = & I_{2} \cdot R_{2} \\ V_{3} & = & I_{3} \cdot R_{3} \end{matrix}

Therefore:

V = I_{1} \cdot R_{1} + I_{2} \cdot R_{2} + I_{3} \cdot R_{3}

However, because

I = I_{1} = I_{2} = I_{3}

, we can further simplify this to:

\begin{matrix} V & = & I \cdot R_{1} + I \cdot R_{2} + I \cdot R_{3} \\ = & I (R_{1} + R_{2} + R_{3}) \end{matrix}

Further, we can write an Ohm's Law relation for the entire circuit:

V = I \cdot R

Therefore:

\begin{matrix} V & = & I (R_{1} + R_{2} + R_{3}) \\ I \cdot R & = & I (R_{1} + R_{2} + R_{3}) \\ ∴ R & = & R_{1} + R_{2} + R_{3} \end{matrix}

Equivalent resistance in a series circuit,

R_{s}

For $n$ resistors in series the equivalent resistance is:

R_{s} = R_{1} + R_{2} + R_{3} + \dots + R_{n}

You can use the following simulation to test this result and all other results in this chapter.

run demo

Let us apply this to the following circuit.

The resistors are in series, therefore:

\begin{matrix} R_{s} & = & R_{1} + R_{2} + R_{3} \\ = & 3 Ω + 10 Ω + 5 Ω \\ = & 18 Ω \end{matrix}

Khan academy video on electric circuits - 1

Two 10 k $Ω$ resistors are connected in series. Calculate the equivalent resistance.

Determine how to approach the problem
Since the resistors are in series we can use:

$R_{s} = R_{1} + R_{2}$
Solve the problem
$\begin{matrix} R_{s} & = & R_{1} + R_{2} \\ = & 10 k Ω + 10 k Ω \\ = & 20 k Ω \end{matrix}$
Write the final answer
The equivalent resistance of two 10 k $Ω$ resistors connected in series is 20 k $Ω$ .

Got questions? Get instant answers now!

Two resistors are connected in series. The equivalent resistance is 100 $Ω$ . If one resistor is 10 $Ω$ , calculate the value of the second resistor.

Determine how to approach the problem
Since the resistors are in series we can use:

$R_{s} = R_{1} + R_{2}$

We are given the value of $R_{s}$ and $R_{1}$ .
Solve the problem
$\begin{matrix} R_{s} & = & R_{1} + R_{2} \\ ∴ R_{2} & = & R_{s} - R_{1} \\ = & 100 Ω - 10 Ω \\ = & 90 Ω \end{matrix}$
Write the final answer
The second resistor has a resistance of 90 $Ω$ .

Got questions? Get instant answers now!

Equivalent parallel resistance

Consider a circuit consisting of a single cell and three resistors that are connected in parallel.

Questions & Answers

I'm interested in biological psychology and cognitive psychology

Tanya Reply

what does preconceived mean

sammie Reply

physiological Psychology

Nwosu Reply

How can I develope my cognitive domain

Amanyire Reply

why is communication effective

Dakolo Reply

Communication is effective because it allows individuals to share ideas, thoughts, and information with others.

effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.

it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.

miss

Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment

Wekolamo Reply

please i need answer

Wekolamo

because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).

Manix Reply

Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!

ARC

A child is a member of community not society elucidate ?

JESSY Reply

Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?

Simon Reply

compare and contrast skinner's perspective on personality development on freud

namakula Reply

Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning

war

explain how nature and nurture affect the development and later the productivity of an individual.

Amesalu Reply

nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.

Samuel

I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills

Zyryn Reply

good👍

Jonathan

and having a good philosophy of the world is like a sandwich and a peanut butter 👍

Jonathan

generally amnesi how long yrs memory loss

Kelu Reply

interpersonal relationships

Abdulfatai Reply

What would be the best educational aid(s) for gifted kids/savants?

Heidi Reply

treat them normal, if they want help then give them. that will make everyone happy

Saurabh

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 11 physical science' conversation and receive update notifications?

Ask

	Biology 302 Final By Dravida Mahadeo-J... Start Quiz
	Social Work midterm By Katy Pratt Start Exam
	2 CDL Quiz - Air Brakes Endorsement Part 2 By Jazzycazz Jackson Start Quiz
	47 Biology 47 Conservation Biology Biodiversity MCQ By OpenStax Start Quiz
	2 Microeconomics 02 Choice in a World of Scarcity By OpenStax Start Flashcards
	6 Arts Society: Theater 6 By Jonathan Long Start Quiz
	2 Neuroscience Exam 2004 3 By David Corey Start Exam
	10 AP Key Terms 10 Muscle Tissue Key Terms By OpenStax Start Key Terms
	17 AP 17 Endocrine System Essay By OpenStax Start Flashcards
	19 Biology 19 The Evolution of Populations MCQ By OpenStax Start Quiz