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By the end of the section, you will be able to:
  • Define the term equivalent resistance
  • Calculate the equivalent resistance of resistors connected in series
  • Calculate the equivalent resistance of resistors connected in parallel

In Current and Resistance , we described the term ‘resistance’ and explained the basic design of a resistor. Basically, a resistor limits the flow of charge in a circuit and is an ohmic device where V = I R . Most circuits have more than one resistor. If several resistors are connected together and connected to a battery, the current supplied by the battery depends on the equivalent resistance    of the circuit.

The equivalent resistance of a combination of resistors depends on both their individual values and how they are connected. The simplest combinations of resistors are series and parallel connections ( [link] ). In a series circuit , the output current of the first resistor flows into the input of the second resistor; therefore, the current is the same in each resistor. In a parallel circuit , all of the resistor leads on one side of the resistors are connected together and all the leads on the other side are connected together. In the case of a parallel configuration, each resistor has the same potential drop across it, and the currents through each resistor may be different, depending on the resistor. The sum of the individual currents equals the current that flows into the parallel connections.

Par a shows four resistors connected in series and part b shows four resistors connected in parallel.
(a) For a series connection of resistors, the current is the same in each resistor. (b) For a parallel connection of resistors, the voltage is the same across each resistor.

Resistors in series

Resistors are said to be in series whenever the current flows through the resistors sequentially. Consider [link] , which shows three resistors in series with an applied voltage equal to V a b . Since there is only one path for the charges to flow through, the current is the same through each resistor. The equivalent resistance of a set of resistors in a series connection is equal to the algebraic sum of the individual resistances.

Part a shows original circuit with three resistors connected in series to a voltage source and part b shows the equivalent circuit with one equivalent resistor connected to the voltage source.
(a) Three resistors connected in series to a voltage source. (b) The original circuit is reduced to an equivalent resistance and a voltage source.

In [link] , the current coming from the voltage source flows through each resistor, so the current through each resistor is the same. The current through the circuit depends on the voltage supplied by the voltage source and the resistance of the resistors. For each resistor, a potential drop occurs that is equal to the loss of electric potential energy as a current travels through each resistor. According to Ohm’s law, the potential drop V across a resistor when a current flows through it is calculated using the equation V = I R , where I is the current in amps (A) and R is the resistance in ohms ( Ω ) . Since energy is conserved, and the voltage is equal to the potential energy per charge, the sum of the voltage applied to the circuit by the source and the potential drops across the individual resistors around a loop should be equal to zero:

Questions & Answers

what is thermodynamics
Aniket Reply
the study of heat an other form of energy.
heat is internal kinetic energy of a body but it doesnt mean heat is energy contained in a body because heat means transfer of energy due to difference in temperature...and in thermo-dynamics we study cause, effect, application, laws, hypothesis and so on about above mentioned phenomenon in detail.
It is abranch of physical chemistry which deals with the interconversion of all form of energy
what is colamb,s law.?
Muhammad Reply
it is a low studied the force between 2 charges F=q.q`\r.r
what is the formula of del in cylindrical, polar media
Birengeso Reply
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
what is flux
Bundi Reply
Total number of field lines crossing the surface area
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
what is temperature change
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
process whereby the degree of hotness of a body (or medium) changes
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
what was the temperature of the soft drink when it was removed ?
15 degree Celsius
15 degree
ok I think is just conversion
15 degree Celsius to Fahrenheit
0 degree Celsius = 32 Fahrenheit
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
I dont understand
the question said you should convert 15 degree Celsius to Fahrenheit
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
what is d final ans for Fahrenheit and Celsius
it said what is temperature change in Fahrenheit and Celsius
the 15 is already in Celsius
So the final answer for Fahrenheit is 59
what is d final ans for Fahrenheit and Celsius
what are the effects of placing a dielectric between the plates of a capacitor
Bundi Reply
increase the capacitance.
besides increasing the capacitance, is there any?
mechanical stiffness and small size
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
Anne Reply
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
Martin Reply
what is flux
Bundi, flux is the number of electric field crossing a surface area
you right
determining dimensional correctness
determine dimensional correctness of,T=2π√L/g
somebody help me answer the question above
calculate the heat flow per square meter through a mineral roll insulation 5cm thick if the temperature on the two surfaces are 30degree Celsius and 20 degree Celsius respectively. thermal conduction of mineral roll is 0.04
akuribire Reply
what are the elementary compositions of a cell?
jackson Reply
poles, chemical
when a current pass through a material does the velocity varies
lovet Reply
what is spin entropy ?and disorder in ferromagnetic material
Nepal Reply
diagram of an hall effect sensor
Aweda Reply
if a magnetised wire having dipole moment M is bent in the form of arc subtending angle of 45°at centre,new magnetic moment is
Pravin Reply
tell the answer
Practice Key Terms 1

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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