Resistors

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.

1. Parallel Combination
2. 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 = I₁ + I₂ + I₃ ----- eq (ii)

Current is divided but the voltage between any two points is same as that of source. This voltage is denoted by V

I₁ = V/R₁ 

I₂ = V/R₂ 

I₃ = V/R₃

By putting values in eq(ii),we have

I_e = V/R₁ + V/R₂ + V/R₃

We know that

I_e = V / R_e  

Where Re is the equivalent resistance of the circuit. So

V / R_e  = V/R₁ + V/R₂ + V/R₃

V(1/R_e) = V(1/R₁ + 1/R₂ + 1/R₃)

1/R_e = 1/R₁ + 1/R₂ + 1/R₃

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/R₁ + 1/R₂ + 1/R₃

Re = R/n  (for resistor having same value)

Where

n = number of resistors

R = value of resistance

R_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/R₁ + 1/R₂ + 1/R₃

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 =IR₁ 

V2 =IR₂

V3 = IR₃

By putting values in eq(i),we have

V = IR₁ +IR₂ + IR₃ ----- eq(ii)

We also know that

V = IRe

So eq(ii) becomes

IR_e = IR₁ +IR₂ + IR₃

IR_e = I(R₁ + R₂ + R₃)

R_e= R₁ + R₂ + R₃

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 = R₁ + R₂ + R₃…. (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 = R₁ + R₂ + R₃

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