Series and Parallel Circuits

Topic of the electric circuits. Series and parallel connected resistors. Finding the equivalent resistance and total current in series and parallel circuits. Subject expression and solved questions.


Series Connected Resistors

In this circuit, the resistors are connect to the same wire. The current is go out from a resistor and come in to other resistor. The resistors are arranged form a chain. In this circuit, the current follow only one path. It is flows through the same current in all of resistors.


The equivalent resistance of n resistors connected in series is found with

Rs = R1 + R2 + R3  + … + Rn 



The current in series circuit is found with

Is = V
Rs




The Resistors in Parallel Connected

The opposite ends of the resistors connected in parallel are merge on the same wire amongst themselves. The current is divide to the arms in the parallel resistors.

The equivalent resistance of n resistors connected in parallel is found with

1 
= 1
+1
+ .. +1
Rn
R2
R1
Rs





If there are two resistors connected in parallel, the equivalent resistance of these resistors can found with

Rs = R1 . R2
R1 + R2




If there are n parallel resistors and magnitude of these resistors are same, the equivalent resistance can found with

Rs = R
n




In this equality, the R is value of any resistor.


Circuits with Series and Parallel Resistors

These circuits have both series and parallel connected resistors. If it is wants to be found of the equivalent resistance of the resistors in the circuit, firstly the equivalent resistance of parallel resistors is found. The equivalent resistance is connected in series to the circuit. Then the value of all resistors is added.

If it is known the current flow or voltage across on any resistors, it can be found the current and voltage of all components in the circuit.


Example:

Seri-paralel-s1i1


Calculate the equivalent resistance and total current in the circuit above.


Solution:

The equivalent resistance of resistors R1 and R2 is

R1,2 = R1•R2
R1 + R2




R1,2 = 12•4
16



R1,2 = 3 Ω


R4, R5 ve R6 dirençlerinin eşdeğeri,

The equivalent resistance of the resistors R4, R5 and R6 is

R4,5,6 = 30 = 10 Ω
3





Now, the circuit has resistors R1-2 , R3, R4-6, R7 and R8. The circuit as follows.

Seri-paralel-s1i2 


The equivalent resistance of the circuit is

R1-8 = 3 + 5 + 10 + 5 + 2

R1-8 = Rs = 25 Ω


Current of the circuit is

Is = 100
25




Is = 4 A


Example:

Seri-paralel-s1i3


Find the equivalent resistance of the circuit in the figure above.

Find the current flowing in through R1, R2, R4 and R7

Calculate the voltage drop across R4 and R7.


Solution:

The equivalent resistance of the resistors R3 and R4 is

R3,4 = 10•15
25



R3,4 = 6 Ω

The R4 and R5 are parallel, the equivalent resistance of these resistors is

R5,6 = 8 = 4 Ω
2




Now, the circuit as following.

Seri-paralel-s1i4


There are resitors R2, R3-4 and R5-6 in the top branch of the circuit. The equivalent resistance of these resistors is

R2-6 = 2 + 6 + 4 = 12 Ω


The R1 and the R2-6 are parallel.

R1-6 = 12•4
16



R1-6 = 3 Ω


The resistor R7 is connected in series to the resistor R1-6.

R1-7 = 3 + 2 = 5 Ω

The equivalent resistance of the circuit.

Rs = 5 Ω

The current drawn from supply source

Is = 60
5



Is = 12 A

The current flowing through resistor R1 is

IR1 = Is•R2-6
R1 + R2-6




IR1 = 12•12
16




IR1 = 9 A


Suppose the current flowing in the upper branch is I2.

I2 = 12 – 9 

I2 = 3 A


The current flowing through the resistor R4 is

IR4 = 3•15
25



IR4 = 1.8 A


The current flowing through the resistor R7 is the main current.

IR7 = 12 A


VR4 = IR4•R4 

VR4 = 1.8•10 = 18 V


VR7 = IR7•R7

VR7 = 12•2 = 24 V


Series-Parallel Circuit Questions And Its Solutions.

Parallel Circuit Questions And Its Solutions.



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02/11/2018

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