Electrical resistance

Resistance definition: Electricity means flowing of electron. If a conductor’s two points has potential difference, then negative charge flows over low voltage to high voltage. Though we know normally current flows from high potential to low potential. At the time of flowing electron makes diffraction in the conductor. As a result flowing current hinders. These types of character of conductor are resistance. It stands that the cause of flowing electric current hinders across a conductor is resistance. This is the definition of resistance. Resistance measurement is easy. Division of total voltage and current is the resistance of a resistor.

From Ohm’s law at specific temperate,

I = V / R
Or, R = V / I

At a specific temperature the division of potential difference and flowing current signifies the resistance. We can measure resistance by it.
S.I resistance unit is Ohm. International unit of flowing current is Ampere (A) and potential difference is volt (V).

So,
1 Ohm = 1V / 1A

Dependence of resistance:
Resistance of conductor depends upon many terms given below

(i) Length of conductor

(ii) Material of conductor

(iii) Temperature of conductor

(iv) Resistance temperature

(v) Area of cross section of conductor

(vi) Effect of Pressure

(vii) Effect of Light

(viii) Effect of Magnet

(ix) Purification of conductor

(x) Resistance heat

Resistances in series

When some resistors are connected such as first resistor’s ending point connects to second resistor’s first point and second resistor’s last point connects to third resistors first point thus some resistors are connected and same current I flows through each resistor. Then we can say the combination is series combination of series resistance.

We consider given figure shown where resistance in a series circuit.

Here R₁and R₂ are connected at B point and R₂and R₃ resistor are connected at C point for resistance series circuit. A is first point of R₁ resistor and D is ending point of R₃ resistor.

Equivalent series resistance:

Consider Voltages of A, B, C and D points are V_A,V_B,V_Cand V_D. Where V_A > V_B

Consider, same current I flows through each resistor. Now applying Ohm’s law different parts in the circuit.

We get,

Between A and B point, V_A – V_B = IR₁

Between B and C point, V_B – V_C = IR₂

Between C and D point, V_C – V_D = IR₃

Adding A to D point,

V_A – V_D = I (R₁+ R₂ + R₃)—————– (i)

If we replace R_1, R₂, and R₃resistance by R_Sas equivalent resistance.

Let, current I flows across the circuit. Then we will get same voltage between A and D point, So R_S is the equivalent resistance of series resistance.

Applying Ohm’s law for resistors series,

V_A – V_D = IR_S ———————- (ii)

From equation (i) & (ii),

IR_S = I (R₁+ R₂ + R₃)

Or, R_S= R₁+ R₂ + R₃ + ———————–+ R_n

This is the equation of resistance in series circuit.

It means sum of all resistance is the equivalent resistance for series combination of resistance.

Resistance in Parallel

Connecting some electrical resistor between two common points having same potential difference for each resistor between two points is known parallel combination of resistors.

Parallel resistance is shown in figure. Here, R_1,R₂, R₃resistors one point is connected at A point and another point is connected at B.

Equivalent resistance: Consider, V_A and V_B are the potential difference of A and B point and V_A>V_B. Total current I supplies. Entering current divides into 3 branches as I₁, I₂, I₃and flow over R_1,R₂, R_3.Then I meet at B point.