# 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

R_{s} = R_{1} + R_{2} + R_{3} + … + R_{n}

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 |
| |||||||||||||

R_{s} |

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

R_{s} = | R_{1} . R_{2} | |

R_{1} + R_{2} |

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

R_{s} = | 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:**

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

**Solution:**

The equivalent resistance of resistors R_{1} and R_{2} is

R_{1,2} = | R_{1}•R_{2} | |

R_{1} + R_{2} |

R_{1,2} = | 12•4 | |

16 |

R_{1,2} = 3 Ω

R_{4}, R_{5} ve R_{6} dirençlerinin eşdeğeri,

The equivalent resistance of the resistors R_{4}, R_{5} and R_{6} is

R_{4,5,6} = | 30 | = 10 Ω |

3 |

Now, the circuit has resistors R_{1-2} , R_{3}, R_{4-6}, R_{7} and R_{8}. The circuit as follows.

The equivalent resistance of the circuit is

R_{1-8} = 3 + 5 + 10 + 5 + 2

R_{1-8} = R_{s} = 25 Ω

Current of the circuit is

I_{s} = | 100 | |

25 |

I_{s} = 4 A

**Example:**

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

Find the current flowing in through R_{1}, R_{2}, R_{4} and R_{7}

Calculate the voltage drop across R_{4} and R_{7}.

**Solution:**

The equivalent resistance of the resistors R_{3} and R_{4} is

R_{3,4} = | 10•15 | |

25 |

R_{3,4} = 6 Ω

The R_{4} and R_{5} are parallel, the equivalent resistance of these resistors is

R_{5,6} = | 8 | = 4 Ω |

2 |

Now, the circuit as following.

There are resitors R_{2}, R_{3-4} and R_{5-6} in the top branch of the circuit. The equivalent resistance of these resistors is

R_{2-6} = 2 + 6 + 4 = 12 Ω

The R_{1} and the R_{2-6} are parallel.

R_{1-6 }= | 12•4 | |

16 |

R_{1-6 }= 3 Ω

The resistor R_{7} is connected in series to the resistor R_{1-6}.

R_{1-7} = 3 + 2 = 5 Ω

The equivalent resistance of the circuit.

R_{s} = 5 Ω

The current drawn from supply source

I_{s }= | 60 | |

5 |

I_{s} = 12 A

The current flowing through resistor R_{1} is

I_{R1} = | I_{s}•R_{2-6} | |

R_{1} + R_{2-6} |

I_{R1} = | 12•12 | |

16 |

I_{R1} = 9 A

Suppose the current flowing in the upper branch is I_{2}.

I_{2} = 12 – 9

I_{2} = 3 A

The current flowing through the resistor R_{4} is

I_{R4} = | 3•15 | |

25 |

I_{R4} = 1.8 A

The current flowing through the resistor R_{7} is the main current.

I_{R7} = 12 A

V_{R4 }= I_{R4}•R_{4}

_{}

V_{R4} = 1.8•10 = 18 V

V_{R7} = I_{R7}•R_{7}

V_{R7} = 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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