1. Home
  2. University physics volume 2
  3. Unit 2. electricity and magnetism
  4. Direct-current circuits
  5. Kirchhoff's rules

10.3 Kirchhoff's rules  (Page 5/10)

<< Chapter < Page
  University physics volume 2     Page 5 / 10
Chapter >> Page >

Check Your Understanding In considering the following schematic and the power supplied and consumed by a circuit, will a voltage source always provide power to the circuit, or can a voltage source consume power?

The figure shows positive terminal of voltage source V subscript 1 of 24 V connected in series to resistor R subscript 1 of 10 kΩ connected in series to positive terminal of voltage source V subscript 2 of 12 V connected in series to resistor R subscript 2 of 30 kΩ.

The circuit can be analyzed using Kirchhoff’s loop rule. The first voltage source supplies power: P in = I V 1 = 7.20 mW. The second voltage source consumes power: P out = I V 2 + I 2 R 1 + I 2 R 2 = 7.2 mW .

Got questions? Get instant answers now!

Calculating current by using kirchhoff’s rules

Find the current flowing in the circuit in [link] .

The figure shows positive terminal of voltage source V subscript 2 of 24 V connected in series to resistor R subscript 3 of 20 Ω connected in series to resistor R subscript 1 of 10 Ω connected in series to positive terminal of voltage source V subscript 1 of 12 V connected in series to resistor R subscript 2 of 30 Ω.
This circuit consists of three resistors and two batteries connected in series. Note that the batteries are connected with opposite polarities.

Strategy

This circuit can be analyzed using Kirchhoff’s rules. There is only one loop and no nodes. Choose the direction of current flow. For this example, we will use the clockwise direction from point a to point b . Consider Loop abcda and use [link] to write the loop equation. Note that according to [link] , battery V 1 will be added and battery V 2 will be subtracted.

Solution

Applying the junction rule yields the following three equations. We have one unknown, so one equation is required:

Loop a b c d a : − I R 1 − V 1 − I R 2 + V 2 − I R 3 = 0 .

Simplify the equations by placing the unknowns on one side of the equations. Use the values given in the figure.

I ( R 1 + R 2 + R 3 ) = V 2 − V 1 . I = V 2 − V 1 R 1 + R 2 + R 3 = 24 V − 12 V 10.0 Ω + 30.0 Ω + 10.0 Ω = 0.20 A .

Significance

The power dissipated or consumed by the circuit equals the power supplied to the circuit, but notice that the current in the battery V 1 is flowing through the battery from the positive terminal to the negative terminal and consumes power.

P R 1 = I 2 R 1 = 0.40 W P R 2 = I 2 R 2 = 1.20 W P R 3 = I 2 R 3 = 0.80 W P V 1 = I V 1 = 2.40 W P dissipated = 4.80 W P source = I V 2 = 4.80 W

The power supplied equals the power dissipated by the resistors and consumed by the battery V 1 .

Got questions? Get instant answers now!

Check Your Understanding When using Kirchhoff’s laws, you need to decide which loops to use and the direction of current flow through each loop. In analyzing the circuit in [link] , the direction of current flow was chosen to be clockwise, from point a to point b . How would the results change if the direction of the current was chosen to be counterclockwise, from point b to point a ?

The current calculated would be equal to I = −0.20 A instead of I = 0.20 A . The sum of the power dissipated and the power consumed would still equal the power supplied.

Got questions? Get instant answers now!

Multiple voltage sources

Many devices require more than one battery. Multiple voltage sources, such as batteries, can be connected in series configurations, parallel configurations, or a combination of the two.

In series, the positive terminal of one battery is connected to the negative terminal of another battery. Any number of voltage sources, including batteries, can be connected in series. Two batteries connected in series are shown in [link] . Using Kirchhoff’s loop rule for the circuit in part (b) gives the result

ε 1 − I r 1 + ε 2 − I r 2 − I R = 0 , [ ( ε 1 + ε 2 ) − I ( r 1 + r 2 ) ] − I R = 0.
Part a shows two batteries connected in series to a resistor. Part b shows the circuit diagram for part a, with each battery represented by an emf source and internal resistance.
(a) Two batteries connected in series with a load resistor. (b) The circuit diagram of the two batteries and the load resistor, with each battery modeled as an idealized emf source and an internal resistance.

Questions & Answers

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
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 2' conversation and receive update notifications?

Ask