Resistors in parallel and series connection

 

Resistors are connected together in circuits to increase or decrease resistance. In circuit boards you can easily observe resistors connected together either in series, parallel or both at a time. So in this eleborate tutorial we shall learn how to calculate total resistance of resistors in parallel and series, current and voltage dividers and total current in circuits. 

Types of resistance connection.

Resistors can only be connected together either in parallel, series or both to form complex network. 

1.Resistors in parallel. 

Resistors are connected to one another ends to ends to form a parallel connection.  When resistors are connected in parallel the total resistance of the connected resistors is smaller than each of them.

In the diagram above you can see that the resistors labelled R followed by number in subscript are connected ends to end, this type of connection is called parralel connection.  To calculate the total resistance(RT) of the above circuit we use this formular; 1/RT=1/R1 + 1/R2 +1/R3. 

Example. 1.

Let's calculate the total resistance in the circuit below.

1/RT=1/R1 + 1/R2 +1/R3. =1/50+1/100+1/500 ohms 

= 0.02+0.01+0.002 

1/RT=0.032 

RT= 1/0.032      

     =31.25ohms.✅

Current and voltage in parallel connection. When resistors are connected together in parallel the current flowing through each of them are different, but they have the same voltage passing through them thus, Vtotal= V1=V2=V3=V4=Vn... For example in the diagram below the current (Itotal) flowing through the circuit is equal to the sum of the total current flowing through each resistor, i.e

Itotal= i1+i2+i3+i4+i5+in+...........

We might want to calculate the current across each resistor, this type of calculation is called current divider. 

E.g current Ix across Rx  can be calculated with the formula; Ix = (Rtotal/Rtotal+Rx)×Itotal 

Where "Itotal" stands for the total current flowing across the circuit. 

Example. 

Calculate the current flowing across each resistor in the circuit below.

 

Solution.

In the circuit above, we were given the voltage source connected to the circuit above as 24v, but the current is not given, so we have to find the Itotal flowing in the whole connection by using our ohms law

" V=IR"   Firstly let's calculate R total,

 1/Rtotal = 1/R1+1/R2+1/R3+1/R4.                      =1/10+1/20+1/30+1/40.                        = 0.1+0.05+0.033+0.025                        =0.208 

Rtotal = 1/0.208 =4.81ohms✅ 

Therefore, 

 Itotal= V/R                                                          =24/4.81             

          = 4.89A.                              

      =5A.✅

Now that we've gotten Itotal let's calculate the current flowing through each resistor.   

a. Current through R1.

I1=(Rtotal/Rtotal+R1)Itotal     

=(4.81/10+4.81)4.89 

=(4.81/14.81)4.89     

= 0.324×4.89    

=~2A.

b. current through R2. 

I2=(Rtotal/Rtotal+R2)Itotal    

  =(4.81/4.81+20)4.89   

 =(4.81/24.81)4.89     

=~1A. 

c. Current through R3. 

I3=(Rtotal/Rtotal+R3)Itotal    

 =(4.81/4.81+30)4.89    

=(4.81/34.81)4.89    

=~1A. 

d. Current through R4. 

I4=(Rtotal/Rtotal+R4)Itotal    

 =(4.81/4.81+40)4.89    

=(4.81/44.81)4.89    

=~1A. 

Since,  Itotal= I1+I2+I3+I4, Then, 2+1+1+1=5A

2. Resistance in series. 

Resistors are connected side by side to form a series connection. The total resistance of each resistors added together is much than each of the resistor's resistance value.

In the circuit diagram above the resistors are connected side by side. The total resistance is  calculated as R1+R2+R3. 

Examples.

1. Calculate the total resistance in the circuit below.

Solutions. RT= R1+R2+R3 Total resistance =3 +10+5 ohms= 18 ohms. Current and voltage in series connection. When resistors are connected together in series across a power supply, the current passing through each resistor is the same because the current that flows through the first resistor will also flow across others, meanwhile the voltage flowing across each resistor is not the same, because the first resistor current will pass through will cause a voltage drop across it. We might also want to calculate the voltage across each resistor, the method use to calculate is called voltage divider. Since the current across each resistors are the same, then V across each resistors can be calculated by multipling Itotal by it resistance Thus Vx=Itotal×resistance value.