Series and Parallel Circuits

Khemraj Nandanwar

T.G.T.(Work Experience)

Kendriya Vidyalaya,Golaghat

Circuits can either be series or parallel.

Series Circuits:-

In Series circuit a number of resistors are connected end to end in such a way that the same current flows through each resistor.

Lights in a Series:-

By adding resistor in a series circuit (Like the another light):-

Total resistance goes UP since all the current has must go through each resistor.

If you remove a light bulb or one burns out—all go out!

Derivation for calulating Total resistance , Total Voltage, Individual voltages, Total current (SERIES):- The circuit in Figure shows three resistors

connected in series, and the direction of current is indicated by the arrow.

Note that since there is only one path for the current to travel, the current through each of the resistors is the same.

(Equation-1)Also, the voltage drops across the resistors must add

up to the total voltage supplied by the battery. (Equation-2)

Since V = I R, then

(Equation-3)

But Ohm's Law must also be satisfied for the complete circuit

(Equation-4)

Setting equations [3] and [4] equal, we get-

We know what the current through each resistor (from equation [1] is just I.

So the currents cancel on both sides, and we arrive at an expression for equivalent resistance for resistors connected in series.

In general, the equivalent resistance of resistors connected in series is the sum of their resistances. That is,

Resistance in SERIES circuits :-

The total or equivalent resistance (RT or Req) for this combination is equal to the sum of the individual resistors, i.e.,

RT = R1+ R2+ R3

Add up all resistors to get Total Resistance.Total resistance will go up because all of the

current must go through each resistor.

Example-1:- Find the total resistance of a series circuit in which 6 ohms,5ohms and 4 ohms resistances are connected.

Answer:-Given data :-R1=6Ω,

R2=5Ω and

R3=4Ω

RT=?

Total Resistance =RT

=R1+R2+R3

= 6+5+4 = 15 Ω

Therefore,Total Resistance=RT

=15 Ω

Voltage in SERIES circuits:-

In series circuit, the voltage is divided at each resistance according to their value.

V1 -Voltage of resistance R1.

V2 – Voltage of resistance R2.

V3 – Voltage of resistance R3.

Total Voltage = V =V1+ V2+ V3

Parallel Circuits:-In Parallel circuit a number of

resistors are arranged in such a way that one end of each resistor is connected to the same one point and the other end of the each resistor is connected to another common point.

Lights in Parallel

By adding resistor in a parallel circuit :-

Total resistance goes down.

If you remove a light bulb or one burns out, the others stay on because the circuit is still closed.

Derivation for calulating Total resistance , Total Voltage, Individual voltage, Total current (PARALLEL):-

Each of the three resistors in Figure is another path for current to travel between points A and B.

Each of the three resistors in the parallel circuit must have the same voltage.

(Equation-1)Also, the current splits as it travels from A to B.

So, the sum of the currents through the three branches is the same as the current at A and at B.

(Equation-2)

By Ohm's Law, equation [2] is equivalent to:

By equation [1], we see that all the voltages are equal.

So the V's cancel out, and we are left with

This result can be generalized to any number of resistors connected in parallel.

Resistance in PARALLEL circuits :-

The formula for the equivalent resistance is as follows:

1/R = 1/R1 + 1/R2 + 1/R3

Example-4:- Find the total resistance of a parallel circuit in which 10 ohms and 20 ohms resistances are connected.

Answer:-Given data :

R1 = 10Ω,

R2 = 20Ω and

RT = ?

Total Resistance =1/RT

=1/R1+1/R2

= (1/10)+(1/20) 1/RT= 3/20

RT= 20/3

RT=6.67 Ω

Therefore,Total Resistance=RT

=6.67 Ω

Example-5:- If the resistances of 6 ohms,3 ohms are connected in parallel. Total voltage is 48V. Calculate the total current and current through each resistance. Answer:-Given data :-R1= 6 Ω,

R2= 3 Ω,

VT= 48V,

IT=?,I1=? And I2=?

Total Resistance = 1/RT=(1/R1)+(1/R2) =(1/6)+(1/3) 1/RT = 1/2 RT = 2 ΩTotal Current = IT = VT/RT = 48/2 = 24 Amp.In Parallel VT = VI = V2 = V3

I1=VT/ R1 = 48/6 = 8 Amp.I2=VT/ R2 = 48/3 = 16 Amp.

OR

In parallel circuit,Total Current=IT= I1 + I2 = 8 + 16 = 24 Amp.

Voltage in Parallel circuits:-In parallel circuit, the voltage across each

resistor is the same, i. e.

V1 -Voltage of resistance R1.

V2 – Voltage of resistance R2.

V3 – Voltage of resistance R3.

Total Voltage = VT = V = V1 = V2 = V3