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But if the cells oppose one another, such as when one is put into an appliance backward, the total emf is less, since it is the algebraic sum of the individual emfs.

A battery is a multiple connection of voltaic cells, as shown in [link] . The disadvantage of series connections of cells is that their internal resistances add. One of the authors once owned a 1957 MGA that had two 6-V batteries in series, rather than a single 12-V battery. This arrangement produced a large internal resistance that caused him many problems in starting the engine.

This diagram shows two typical batteries in series, with the positive terminal of the first touching the negative terminal of the second. The schematic diagram of the electric current flowing through them is shown as current I passing through the series of two cells of e m f script E sub one and internal resistance r sub one and e m f script E sub two and internal resistance r sub two.
A series connection of two voltage sources. The emfs (each labeled with a script E) and internal resistances add, giving a total emf of emf 1 + emf 2 size 12{"emf" rSub { size 8{1} } +"emf" rSub { size 8{2} } } {} and a total internal resistance of r 1 + r 2 size 12{r rSub { size 8{1} } +r rSub { size 8{2} } } {} .
The left side of the diagram shows a battery that contains a combination of a large number of cells. The right side shows a set of cells combined in series to form a battery.
Batteries are multiple connections of individual cells, as shown in this modern rendition of an old print. Single cells, such as AA or C cells, are commonly called batteries, although this is technically incorrect.

If the series connection of two voltage sources is made into a complete circuit with the emfs in opposition, then a current of magnitude I = emf 1 emf 2 r 1 + r 2 size 12{I= { { left ("emf" rSub { size 8{1} } - "emf" rSub { size 8{2} } right )} over {r rSub { size 8{1} } +r rSub { size 8{2} } } } } {} flows. See [link] , for example, which shows a circuit exactly analogous to the battery charger discussed above. If two voltage sources in series with emfs in the same sense are connected to a load R load size 12{R rSub { size 8{"load"} } } {} , as in [link] , then I = emf 1 + emf 2 r 1 + r 2 + R load size 12{I= { { left ("emf" rSub { size 8{1} } - "emf" rSub { size 8{2} } right )} over {r rSub { size 8{1} } +r rSub { size 8{2} } +R rSub { size 8{"load"} } } } } {} flows.

The diagram shows a closed circuit containing series connection of two cells of e m f script E sub one and internal resistance r sub one and e m f script E sub two and internal resistance r sub two. The positive end of E sub one is connected to the positive end of E sub two.
These two voltage sources are connected in series with their emfs in opposition. Current flows in the direction of the greater emf and is limited to I = emf 1 emf 2 r 1 + r 2 size 12{I= { { left ("emf" rSub { size 8{1} } - "emf" rSub { size 8{2} } right )} over {r rSub { size 8{1} } +r rSub { size 8{2} } } } } {} by the sum of the internal resistances. (Note that each emf is represented by script E in the figure.) A battery charger connected to a battery is an example of such a connection. The charger must have a larger emf than the battery to reverse current through it.
Part a shows a flashlight glowing when connected to two cells joined in series with the positive end of one cell connected to the negative end of the other. Part b shows the schematic circuit for part a. There is a series combination of two cells of e m f script E sub one and internal resistance r sub one and e m f script E sub two and internal resistance r sub two connected to a load resistor R sub load.
This schematic represents a flashlight with two cells (voltage sources) and a single bulb (load resistance) in series. The current that flows is I = emf 1 + emf 2 r 1 + r 2 + R load size 12{I= { { left ("emf" rSub { size 8{1} } - "emf" rSub { size 8{2} } right )} over {r rSub { size 8{1} } +r rSub { size 8{2} } +R rSub { size 8{"load"} } } } } {} . (Note that each emf is represented by script E in the figure.)

Take-home experiment: flashlight batteries

Find a flashlight that uses several batteries and find new and old batteries. Based on the discussions in this module, predict the brightness of the flashlight when different combinations of batteries are used. Do your predictions match what you observe? Now place new batteries in the flashlight and leave the flashlight switched on for several hours. Is the flashlight still quite bright? Do the same with the old batteries. Is the flashlight as bright when left on for the same length of time with old and new batteries? What does this say for the case when you are limited in the number of available new batteries?

[link] shows two voltage sources with identical emfs in parallel and connected to a load resistance. In this simple case, the total emf is the same as the individual emfs. But the total internal resistance is reduced, since the internal resistances are in parallel. The parallel connection thus can produce a larger current.

Questions & Answers

does the force in a system result in the energy transfer?
Lebatam Reply
full meaning of GPS system
Anaele Reply
how to prove that Newton's law of universal gravitation F = GmM ______ R²
Kaka Reply
sir dose it apply to the human system
Olubukola Reply
prove that the centrimental force Fc= M1V² _________ r
Kaka Reply
prove that centripetal force Fc = MV² ______ r
Kaka
how lesers can transmit information
mitul Reply
griffts bridge derivative
Ganesh Reply
below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
Timothy Reply
what is a conductor
Timothy
hello
Timothy
below me
why below you
Timothy
no....I said below me ...... nothing below .....ok?
dust particles contains both positive and negative charge particles
Mbutene
corona charge can verify
Stephen
when pressure increases the temperature remain what?
Ibrahim Reply
remains the temperature
betuel
what is frequency
Mbionyi Reply
define precision briefly
Sujitha Reply
CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.
MITHRA Reply
hope this helps
what's critical angle
Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
dude.....next time Google it
okay whatever
Chidalu
pls who can give the definition of relative density?
Temiloluwa
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
Chidalu
What is momentum
aliyu Reply
mass ×velocity
Chidalu
it is the product of mass ×velocity of an object
Chidalu
how do I highlight a sentence]p? I select the sentence but get options like copy or web search but no highlight. tks. src
Sean Reply
then you can edit your work anyway you want
Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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