**Resistors**

**What are resistors?**

These are just like hurdles, as hurdles are placed to slow down racer on a track similarly resistors are placed in a circuit to slow the motion of electrons.

As we define resistor as:

**“Any piece of wire or any device that resist the flow of current is called resistor.”**

A german scientist Ohm gave ohms law to describe relation between current,resistance and voltage.

V=IR ----- eq (i)

So when current increases resistance decreases and vice versa.

Resistors are connected in following different combinations.

- Parallel Combination
- Series Combination

**Parallel Combination:**

Parallel means side by side so when resistors are connected head to head this is called as parallel combination of resistors.

As it is clear from the figure, current coming from a single source get more than one path to pass so current is divided in such a combination.But here we use equivalent current which is denoted by symbol Ie and is given as

Ie = I

_{1 }+ I_{2 }+ I_{3}----- eq (ii)
Current is divided but the voltage between any two points is same as that of source. This voltage is denoted by V

I

_{1 }= V/R_{1}
I

_{2 }= V/R_{2}
I

_{3}= V/R_{3}
By putting values in eq(ii),we have

I

_{e}= V/R_{1}+ V/R_{2}+ V/R_{3}
We know that

I

_{e}= V / R_{e}
Where Re is the equivalent resistance of the circuit. So

V / R

_{e}= V/R_{1}+ V/R_{2}+ V/R_{3}
V(1/R

_{e}) = V(1/R_{1}+ 1/R_{2}+ 1/R_{3})
1/R

_{e}= 1/R_{1}+ 1/R_{2}+ 1/R_{3}
So the equivalent resistance is the resistance which circuit impose and more logically it is obvious that the value of equivalent resistance is less then the smallest known resistance in the circuit. When we have a number of resistors having high values,we connect them in parallel to get smallest value.

Different formulas to calculate Re:

1/R

_{e}= 1/R_{1}+ 1/R_{2}+ 1/R_{3}
Re = R/n (for resistor having same value)

Where

n = number of resistors

R = value of resistance

R

(for two resistors having different value)

_{e}= R1+R2 / R1R2(for two resistors having different value)

**Example 1:**

__Calculate Re in above combination?__

As we know that

1/R

_{e}= 1/R_{1}+ 1/R_{2}+ 1/R_{3}
1/R

_{e}= 1/2 + 1/3 + 1/4
1/R

_{e}= 13/12
R

_{e}= 12/13
R

_{e}= 0.92 ohm**Example 2:**

__Calculate Re in above combination?__

As we know for same resistors

R

_{e}= R/n
R

_{e}= 2/3
R

_{e}= 0.66 ohm**Example 3:**

__Calculate Re in above combination?__

As we know for different resistors

R

_{e}= R1+R2/R1R2
R

_{e}= 4+5/4x5
R

_{e}= 9/20
R

_{e}= 0.45 ohm**Series Combination:**

Series means in a row.When resistors are connected end to end it is called series combination.In this combination same current passes through each resistor but voltage divides across each resistor. So the voltage of source is V which appears as

V = V1 + V2 + V3 ----- eq(i)

We know that

V1 =IR

_{1}
V2 =IR

_{2}
V3 = IR

_{3}
By putting values in eq(i),we have

V = IR

_{1}+IR_{2}+ IR_{3}----- eq(ii)
We also know that

V = IRe

So eq(ii) becomes

IR

_{e}= IR_{1}+IR_{2}+ IR_{3}
IR

_{e}= I(R_{1}+ R_{2}+ R_{3})
R

_{e}= R_{1}+ R_{2}+ R_{3}
So this is the equivalent resistance of series combination and is the sum of all resistance. So when we have a number of small resistance we connect them in series to get higher resistance. The equivalent resistance is greater than highest resistance in circuit.

__Formulas to calculate Re:__

R

_{e}= R_{1}+ R_{2}+ R_{3}…. (for different resistances)
R

_{e}= nR (for same resistance)
Where

R = any resistance

n = number of resistance

**Example 1:**

__Calculate Re for above combination?__

As we know that for different resistance

R

_{e}= R_{1}+ R_{2}+ R_{3}
R

_{e}= 2+3+4
R

_{e}= 9 ohm**Example 2:**

__Calculate Re for above combination?__

As we know that for same resistance

R

_{e}= nR
R

_{e }= 3x3 ohm
R

_{e}= 9 ohm
Animation:

**Entry # 4**

**By Muhammad Hafeez**

10/10

ReplyDelete8/10

ReplyDeleteif a resistance R is cut into 4 parts,then these parts are connected in

ReplyDeleteseries ans parallel combination,then what will resistance in these both

cases separately.?explain.

As resistance is.propotional to length as length of each part decreases by4 so resistance of each will be R/4 and thn find the equivalent resistqnce by formulas of parallel ans series.resistance

ReplyDelete8

ReplyDeletegood info for students