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 7/10)

<< Chapter < Page
  University physics volume 2     Page 7 / 10
Chapter >> Page >

Solar cell arrays

Another example dealing with multiple voltage sources is that of combinations of solar cells —wired in both series and parallel combinations to yield a desired voltage and current. Photovoltaic generation, which is the conversion of sunlight directly into electricity, is based upon the photoelectric effect. The photoelectric effect is beyond the scope of this chapter and is covered in Photons and Matter Waves , but in general, photons hitting the surface of a solar cell create an electric current in the cell.

Most solar cells are made from pure silicon. Most single cells have a voltage output of about 0.5 V, while the current output is a function of the amount of sunlight falling on the cell (the incident solar radiation known as the insolation). Under bright noon sunlight, a current per unit area of about 100 mA/cm 2 of cell surface area is produced by typical single-crystal cells.

Individual solar cells are connected electrically in modules to meet electrical energy needs. They can be wired together in series or in parallel—connected like the batteries discussed earlier. A solar-cell array or module usually consists of between 36 and 72 cells, with a power output of 50 W to 140 W.

Solar cells, like batteries, provide a direct current (dc) voltage. Current from a dc voltage source is unidirectional. Most household appliances need an alternating current (ac) voltage.

Summary

  • Kirchhoff’s rules can be used to analyze any circuit, simple or complex. The simpler series and parallel connection rules are special cases of Kirchhoff’s rules.
  • Kirchhoff’s first rule, also known as the junction rule, applies to the charge to a junction. Current is the flow of charge; thus, whatever charge flows into the junction must flow out.
  • Kirchhoff’s second rule, also known as the loop rule, states that the voltage drop around a loop is zero.
  • When calculating potential and current using Kirchhoff’s rules, a set of conventions must be followed for determining the correct signs of various terms.
  • When multiple voltage sources are in series, their internal resistances add together and their emfs add together to get the total values.
  • When multiple voltage sources are in parallel, their internal resistances combine to an equivalent resistance that is less than the individual resistance and provides a higher current than a single cell.
  • Solar cells can be wired in series or parallel to provide increased voltage or current, respectively.

Conceptual questions

Can all of the currents going into the junction shown below be positive? Explain.

The figure shows a junction with three incoming current branches.
Got questions? Get instant answers now!

Consider the circuit shown below. Does the analysis of the circuit require Kirchhoff’s method, or can it be redrawn to simplify the circuit? If it is a circuit of series and parallel connections, what is the equivalent resistance?

The figure shows a circuit with positive terminal of voltage source V connected to three parallel branches. The first branch has resistor R subscript 2 connected to parallel branches with R subscript 4 and R subscript 3 series with R subscript 5. The second branch has resistor R subscript 1 and third branch has resistor R subscript 6.

It can be redrawn.
R eq = [ 1 R 6 + 1 R 1 + 1 R 2 + ( 1 R 4 + 1 R 3 + R 5 ) −1 ] −1

Got questions? Get instant answers now!

Do batteries in a circuit always supply power to a circuit, or can they absorb power in a circuit? Give an example.

Got questions? Get instant answers now!

What are the advantages and disadvantages of connecting batteries in series? In parallel?

In series the voltages add, but so do the internal resistances, because the internal resistances are in series. In parallel, the terminal voltage is the same, but the equivalent internal resistance is smaller than the smallest individual internal resistance and a higher current can be provided.

Got questions? Get instant answers now!

Semi-tractor trucks use four large 12-V batteries. The starter system requires 24 V, while normal operation of the truck’s other electrical components utilizes 12 V. How could the four batteries be connected to produce 24 V? To produce 12 V? Why is 24 V better than 12 V for starting the truck’s engine (a very heavy load)?

Got questions? Get instant answers now!

Problems

Consider the circuit shown below. (a) Find the voltage across each resistor. (b)What is the power supplied to the circuit and the power dissipated or consumed by the circuit?

The figure shows positive terminal of voltage source V subscript 1 of 12 V connected in series to resistor R subscript 1 of 10 kΩ connected in series to resistor R subscript 2 of 20 kΩ connected in series to resistor R subscript 3 of 10 kΩ connected in series to positive terminal of voltage source V subscript 2 of 24 V connected in series to resistor R subscript 4 of 10 kΩ connected in series to resistor R subscript 5 of 10 kΩ.
Got questions? Get instant answers now!

Consider the circuits shown below. (a) What is the current through each resistor in part (a)? (b) What is the current through each resistor in part (b)? (c) What is the power dissipated or consumed by each circuit? (d) What is the power supplied to each circuit?

Part a shows positive terminal of voltage source V subscript 1 of 1.6 V connected to parallel branches, one with resistor R subscript 1 of 2 kΩ and second with positive terminal of voltage source V subscript 2 of 1.4 V and resistor R subscript 3 of 1 kΩ. The two branches are connected back to V subscript 1 through resistor R subscript 2 of 1 kΩ. Part b shows the same circuit as part a but the terminals of V subscript 2 are reversed.

a. I 1 = 0.6 mA , I 2 = 0.4 mA , I 3 = 0.2 mA ;
b. I 1 = 0.04 mA , I 2 = 1.52 mA , I 3 = −1.48 mA ; c. P out = 0.92 mW , P out = 4.50 mW ;
d. P in = 0.92 mW , P in = 4.50 mW

Got questions? Get instant answers now!

Consider the circuit shown below. Find V 1 , I 2 , and I 3 .

The positive terminal of voltage source V subscript 1 is connected to resistance R subscript 1 of 12 Ω with right current I subscript 1 of 2 A connected to two parallel branches, first with resistor R subscript 2 of 6 Ω with upward current I subscript 2 and second with right current I subscript 3, negative terminal of voltage source V subscript 2 of 21 V and resistor R subscript 3 of 5 Ω.
Got questions? Get instant answers now!

Consider the circuit shown below. Find V 1 , V 2 , and R 4 .

The figure shows a circuit with three horizontal branches. The first branch has resistor R subscript 1 of 6 Ω with right current I subscript 1 of 4 A. The second branch has resistor R subscript 2 of 4 Ω with left current I subscript 2 of 3 A and resistor R subscript 3 of 6 Ω with left current I subscript 3 of 1 A. The third branch has resistor R subscript 5 of 4 Ω with left current I subscript 5 of 3 A. The first and second horizontal branches are connected on the right directly and on the left with voltage source V subscript 1 with positive terminal connected to first branch. The second and third horizontal branches are connected on the right directly and on the left with resistor R subscript 4 with upward current I subscript 4 of 1 A. The second and third branches are also connected in the middle with a voltage source V subscript 2 with positive terminal connected to second branch.

V 1 = 42 V , V 2 = 6 V , R 4 = 6 Ω

Got questions? Get instant answers now!

Consider the circuit shown below. Find I 1 , I 2 , and I 3 .

The positive terminal of voltage source V subscript 1 of 24 V is connected to two parallel branches. The first branch has resistor R subscript 1 of 8 Ω with downward current I subscript 1 and second branch connects to positive terminal of voltage source V subscript 2 of 10 V and resistor R subscript 3 of 4 Ω with left current I subscript 3. The two branches are connected to V subscript 1 through resistor R subscript 2 of 6 Ω with left current of I subscript 2.
Got questions? Get instant answers now!

Consider the circuit shown below. (a) Find I 1 , I 2 , I 3 , I 4 , and I 5 . (b) Find the power supplied by the voltage sources. (c) Find the power dissipated by the resistors.

The circuit has four vertical branches. From left to right, first branch has voltage source V subscript 1 of 12 V with positive terminal upward. The second branch has resistor R subscript 1 of 4 Ω with downward current I subscript 1. The third branch has voltage source V subscript 2 of 5 V with positive terminal upward and upward current I subscript 5. The fourth branch has resistor R subscript 4 of 2 Ω with downward current I subscript 4. The first and second branch are connected at the bottom through resistor R subscript 2 of 3 Ω with left current I subscript 2 and second and third branch are connected at the bottom through resistor R subscript 3 of 2 Ω with left current I subscript 3.

a. I 1 = 1.5 A , I 2 = 2 A , I 3 = 0.5 A , I 4 = 2.5 A , I 5 = 2 A ; b. P in = I 2 V 1 + I 5 V 5 = 34 W ;
c. P out = I 1 2 R 1 + I 2 2 R 2 + I 3 2 R 3 + I 4 2 R 4 = 34 W

Got questions? Get instant answers now!

Consider the circuit shown below. Write the three loop equations for the loops shown.

The circuit has four vertical branches. From left to right, first branch has voltage source V subscript 1 with positive terminal upward. The second branch has resistor R subscript 2 with downward current I subscript 2. The third branch has voltage source V subscript 2 with positive terminal upward and downward current I subscript 2. The fourth branch has resistor R subscript 5 with downward current I subscript 5. The first and second branch are connected at the bottom through resistor R subscript 1 and second and third branch are connected at the bottom through resistor R subscript 4 with left current I subscript 4. The second and third branch are connected at the top through resistor R subscript 3 with left current I subscript 3. The current at the top between first and second branch is right I subscript 1.
Got questions? Get instant answers now!

Consider the circuit shown below. Write equations for the three currents in terms of R and V .

The circuit has four vertical branches. From left to right, first branch has voltage source V subscript 1 with positive terminal upward and resistor R. The second branch has resistor R with downward current I subscript 1. The third and fourth branches both have resistor 2 R and are connected to positive terminal of another voltage source V. The current between first and second branch is right I subscript 2 and between second and third branch is left I subscript 3.

I 1 = 3 5 V R , I 2 = 2 5 V R , I 3 = 1 5 V R

Got questions? Get instant answers now!

Consider the circuit shown in the preceding problem. Write equations for the power supplied by the voltage sources and the power dissipated by the resistors in terms of R and V .

Got questions? Get instant answers now!

A child’s electronic toy is supplied by three 1.58-V alkaline cells having internal resistances of 0.0200 Ω in series with a 1.53-V carbon-zinc dry cell having a 0.100 - Ω internal resistance. The load resistance is 10.0 Ω . (a) Draw a circuit diagram of the toy and its batteries. (b) What current flows? (c) How much power is supplied to the load? (d) What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?

a.
The resistor R subscript L is connected in series with resistor r subscript 2, voltage source ε subscript 2, resistor r subscript 1, voltage source ε subscript 1, resistor r subscript 1, voltage source ε subscript 1, resistor r subscript 1and voltage source ε subscript 1. All voltage sources have upward negative terminals. ;
b. 0.617 A; c. 3.81 W; d. 18.0 Ω

Got questions? Get instant answers now!

Apply the junction rule to Junction b shown below. Is any new information gained by applying the junction rule at e ?

The circuit has three vertical branches. From left to right, first branch has voltage source ε subscript 1 of 18 V and internal resistance 0.5 Ω with positive terminal upward. The second branch has resistor R subscript 2 of 6 Ω with downward current I subscript 3 and voltage source ε subscript 2 of 3 V and internal resistance 0.25 Ω with positive terminal downward. The third branch has voltage source ε subscript 3 of 12 V and internal resistance 0.5 Ω with positive terminal downward. The first and second branch are connected at the top through resistor R subscript 1 of 20 Ω with right current I subscript 1 and bottom through resistor R subscript 4 of 15 Ω. The second and third branch are connected at the top through resistor R subscript 3 of 8 Ω with right current I subscript 2 and bottom through voltage source ε subscript 4 of 18 V with right positive terminal and internal resistance 0.75 Ω.
Got questions? Get instant answers now!

Apply the loop rule to Loop afedcba in the preceding problem.

I 1 r 1 − ε 1 + I 1 R 4 + ε 4 + I 2 r 4 + I 4 r 3 − ε 3 + I 2 R 3 + I 1 R 1 = 0

Got questions? Get instant answers now!

Questions & Answers

prostaglandin and fever
Maha Reply
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
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