Series and Parallel combination of Resistance 

When the resistor is connected in series to any circuit, the resistance of the circuit increases. I would like you to understand this whole process in detail. Friends, these combinations are actually 2 types.

1) Series combination 2) Parallel combination

1) Series combination

When resistance is connected in series, the value of resistance increases. Which increases the equivalent resistance of the circuit. How will it be known whether resistance is in series or not. Friends, always remember that if there is resistance series, the voltage will always be different and the current will always be the same.

Resistance in series

   The formula for Equivalent resistance in Series combination is like this

R = R1 + R2 + R3

 Now how and where did it come from. Some mathematical proof of it is like this.

We can say that…

 V = V1 + V2 + V3 ---------- (1)

According to Ohm's Law ---->

 V = I R

 So this is the Series combination, in this the current will always be the same but the voltage will always be different. So we will keep the value of V of Ohm's Law in eq (1).

  V = V1 + V2 + V3

I R = IR1 + IR2 + IR3

IR = I (R1 + R2 + R3)

 R = R1 + R2 + R3

 R = Equivalent resistance

Numerical----

Q = If R1 = 6Ω, R2 = 4Ω. If these resistance in connected in series, then calculate its equivalent resistance?

Solution=> R=Equivalent resistance

          R = R1 + R2

 R = 6Ω + 4Ω

R = 10Ω

2)  Parallel combination

When resistance is connected in parallel, the value of resistance decreases. Which reduces the equivalent resistance of the circuit. How to know whether resistance is in parallel or not. Friends, always remember that if there is resistance series, the voltage will always be the same and the current will always be different.

Resistance in parallel

 The formula for equivalent resistance in parallel combination is like this

  R = 1 / R1 + 1 / R2 + 1 / R3

 Now how and where did it come from. Some mathematical proof of it is like this.

We can say that…

 I = I1 + I2 + I3 ---------- (1)

According to Ohm's Law ---->

 V = I R

 I = V / R

 So this is a parallel combination, in this the current will always be different but the voltage will always be the same. So we will keep the value of I of Ohm's Law in eq (1).

  I = I1 + I2 + I3

V / R = V / R1 + V / R2 + V / R3

 V / R = V (1 / R1 + 1 / R2 + 1 / R3)

 R = 1 / R1 + 1 / R2 + 1 / R3

 R = Equivalent resistance

 

Numerical----

Q = If R1 = 10Ω, R2 = 10Ω. If these resistance in connected in parallel, then calculate its equivalent resistance?

Solution=> R=Equivalent resistance

                R = 1/R1 + 1/R2

 R = 1/10Ω + 1/10Ω

R = 5Ω

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Ishan Kumar