## electrical resistance in a circuit

In a circuit electrical Resistance is the property of a conductor which opposes the flow of current and its property is called resistivity. The S.I unit of electrical resistance is ohm indicates symbol as (**Ω)**.In mathematically electrical resistance is dedicated as

**R=V/I**

**Where R=resistance V=voltage I=current**

**Laws of Electrical Resistance**

The value of resistance of a conductor or insulator depends upon the following factors:

- Electrical Resistance of a conductor is directly proportional to the length of the conductor or insulator.
- The value of electrical Resistance of a conductor is inversely proportional to the area of cross section of the conductor.
- The electrical resistance of any conductor depends upon the type of material or the resistivity of that conductor.

**Resistivity or Specific Resistance**

Every conductor depending upon its shape and size opposes the flow of current flowing through the body, this opposition to the flow of current is called resistivity.

In the formula**, R=Pl/A**

**If l=1cm R=p A=1cm ^{2}**

Hence the electrical resistance of a conductor of 1cm in length having a cross-sectional area of 1cm^{2} is called specific resistance of that conductor.

#### Unit of specific resistance

By formula R=pl/A

P=RA/l=ohm*cm^{2}/cm0

=ohm-cm or Ω-cm

Hence unit of specific resistance is Ω-cm and in MKS it is Ω-m

** ****Temprature co-efficient of electrical resistance**

The electrical resistance of almost all electricity conducting materials change with the variation in temperature. This variation of resistance with change in temperature is governed by a property of a material called temperature coefficient of resistance.

The temperature coefficient of resistance can be defined as the change in electrical resistance per degree change in temperature and expressed as a fraction of the resistance at the reference temperature considered. If the value of resistance is R_{t}=R_{0}(1+ἀ_{0}t)

Therefore temperature coefficient, ἀ_{0}=R_{t}-R_{0}/R_{0}t

And ἀ_{t}=ἀ_{0}/1+ἀ_{0}t

Here ἀ_{0}=temperature coefficient at 0^{0}C

Now we will consider different cases

- If the value of temperature coefficient is positive then the value of electrical resistance increases with the increase in temperature.
- the value of temperature coefficient is negative then the value of electrical resistance decreases with increase in temperature.
- If the value of electrical resistance is known at certain temperature then the value of resistance at other temperature can also be calculated.

Suppose, t_{1}=initial temperature (in ^{0}c)

T_{2}=final temperature (in ^{0}c)

R_{t1}=value of resistance at t^{0}_{1} C (in ohm)

R_{t2}=value of resistance at t^{0}_{2}C (in ohm)

ἀ=temperature coefficient at 0^{0}C (per ^{0}C)

R_{0}=resistance at 0^{0}C (in ohm).

Hence R_{t1}=R_{0}(1+ἀt_{1})

R_{t2}=R_{0}(1+ἀt_{2})

** ****From eq. (i) and (ii) we get**

R_{t2}/R_{t1}=R_{0}(1+ἀt_{2})/R_{0}(1+ἀt_{1})

Hence R_{t2}=R_{t1}(1+ἀt_{2})/(1+ἀt_{1})

** ****Unit of temperature coefficient **

From the formula ἀ_{0}=R_{t}-R_{0}/R_{0}t

=ohm/ohm*^{0}C=1/^{0}C=per ^{0}C

** ****How we can find the value of electrical resistance **

Normally the value of electrical resistance and wattage is specified on the resistor itself. But the size of carbon resistance is so small hence marking the value is not easy. For the convenience of marking the value of carbon resistor they are of band type and body type.

**Band type**

In this method four colour rings or bands are made from one end on the body of resistor. First ring represents first letter of the resistance value second ring represents second letter of the electrical resistance value third ring represents multiple and fourth ring represents the tolerance of the resistance value.

**Body type**

In this method complete body of electrical resistance is coloured with one colour. One end of the resistance is colored with other colour and a circular and a rectangular mark is also made of different colour. The body colour represents the first letter of the resistance value colour at one end represents the second letter of the resistance value circular dot represents the multiple and rectangular mark represents its tolerance value.

**The table below gives the value of different value of colours at their respective positions:**

colour value for resistance |
||||

colour |
first band |
second band |
third band |
fourth band |

Black | 0 | 0 | 1 | − |

Brown | 1 | 1 | 10 | ±1% |

Red | 2 | 2 | 100 | ±2% |

Orrange | 3 | 3 | 1000 | ±3% |

Yellow | 4 | 4 | 10000 | ±4% |

Green | 5 | 5 | 100000 | − |

Blue | 6 | 6 | 1000000 | − |

Violet | 7 | 7 | − | − |

Grey | 8 | 8 | − | − |

White | 9 | 9 | − | − |

Golden | − | − | 0.1 | ±15% |

Silver | − | − | 0.01 | ±10% |

No Colour | − | − | − | ±20% |

** **

**From the above table an example of colour combination of resistance and their value accordingly is explained below:**

**Value of electrical resistance according to colour combination**

** **

S.No. | First Ring | Second Ring | Third Ring | Fourth Ring | Resistance value |

1 | Red | Black | Golden | Golden | 2.0Ω ±5% |

2 | Red | Yellow | Black | Red | 24Ω ±2% |

3 | Red | violet | Orange | Silver | 27kΩ ±10% |

4 | Yellow | violet | yellow | Golden | 1470kΩ ±5% |

5 | Brown | Black | Green | Golden | 1MΩ ±5% |

6 | Brown | Black | Blue | Silver | 10MΩ ±10% |

** **

**Direct method of finding the electrical resistance value**

For the range of ½ to 2W resistance value of resistance can be directly written on the resistance in the form of codes where R=1 K=10^{3} and M=10^{6}

e.g R 24 = 0.24Ω

2R 5 = 2.5 Ω

3K 2 = 3.2 k Ω

M 5= 0.5 M Ω

1M 2= 1.2 M Ω

Here in place of decimals a letter is used**.**

### Groupings of electrical resistance

When a certain value of resistance is required which cannot be obtained by conventional methods of manufacturing .then the required value of electrical resistance can be obtained by connecting resistance in series or in parallel groups.

** series grouping of electrical resistance**

The resistance are said to be in series group if the same current flows in the resistors. In series grouping, the voltage drop across each resistance is different and total voltage drop (V_{r}) across the circuit is equal to the sum of individual voltage drops.

In mathematically

V_{r}=V_{1}+V_{2}+V_{3}+…..+V_{n}

Now, according to ohm’s law,

V=IR

V_{r}=IR_{1}+ IR_{2}+ IR_{3}…..+ IR_{n}

Since the value of current is same in series grouping

Or V_{r}/I=R_{1}+R_{2}+R_{3}….+R_{n}

Equivalent resistance,R_{r}= R_{1}+R_{2}+R_{3}+…+R_{n}

In this way,equivalent resistance (R_{r} or R_{eq}) of any number of resistors connected in series is the sum of the individual resistance.

i.e, for n resistance connected in series grouping.

R_{eq} or R_{r} =R_{1}+R_{2}+….+R_{n} =Σ

**Parallel grouping of electrical resistance**

The resistance is said to be in parallel group, if the voltage drop across each resistor is same. In parallel group the current across each resistor is different and total current flown is equal to the sum of the current flown in each resistor

Mathematically,

Ir=I1+I2+I3+…+In

Now according to ohm’s law

Ir = + + +…+

Value of voltage drop is same in parallel grouping or

Ir= V ( + + +…+ ) ⁄=( + + +…+ )

=( + + +…+ )

In this way equivalent resistance Rr orReq of any number of visitors connected in parallel.

For n resistors connected in parallel grouping, the equivalent

**Mixed grouping of electrical resistance**

when series groupings and parallel groupings are combined together they form mixed groupings.mixed grouping is further of two types:-

- parallel-series grouping
- series-parallel grouping

when series groups are connected in parallel then the grouping formed is series-parallel grouping series-parallel groupings of electrical resistance are shown below

#### parallel-series grouping of electrical resistance

when parallel groups are connected in series then this grouping formed is parallel-series grouping of electrical resistance as shown in figure below

#### series-parallel grouping of electrical resistance

when series groups are connected in parallel then the grouping formed is series-parallel groupings. series-parallel grouping of electrical resistance as shown in figure below

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