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Electric Circuit

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An Electric Circuit is a interconnection of circuit elements. There are two things that are important
  • Circuit elements themselves
  • The way they are connected
It comprises of an arrangement of elements, conversion and transmission and storage of energy. The rate at which it flows is called as current, the greater the current the more energy is transmitted.

Electric Circuit Definition

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An Electric Circuit is defined as the path in which electrons flow from a voltage or current source. The point where electrons starts flowing is called source and where the electrons leave the circuit is called ground (or earthed). Lets go through a simple electric circuit,
Electric Circuit
The diagram using has electric components to describe an electrical circuit like source S and resistance R.

Electric Circuit theory

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To begin with electric circuit theory there are many electric components such as any lamp, a heater, a key, a wire etc connected to a battery that acts as source in such a way that the electrons flow ends to some point known as ground.

Types of Electric Circuits

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The electrical circuits are of two types :
  • Open circuit
  • Closed circuit
Open electrical circuit is that where the electric current does not flow because the key is open or the switch is off whereas closed electrical circuit is the circuit in which the electric current flows because the key is closed or switch is on.
Its known that current flows in a conductor when a potential difference is maintained across its ends. How much it is? was a question.This was given by German scientist Simon Ohm, by his experiments who found a relationship between the potential difference and current in a conductor. This relationship is known as Ohm’s law.
Ohm's Law states as,
The current that flows through the conductor varies directly to the potential across its ends if temperature and other physical conditions are kept constant.

Ohms Law
If V is the voltage applied across the ends of a conductor then the current flowing through it is given by,
I = $\frac{V}{R}$
Where,
V = voltage applied across its ends
I is current flow
R is resistance offered by conductor.
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Kirchhoff's Voltage Law

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It was given by Gustav R. Kirchhoff, a German physicist discovered the principle of the voltage law also known as Kirchhoff Second Law (KVL) which states that "The algebraic sum of the voltage (potential) differences in any loop must equal zero".
Kirchhoff's Voltage Law
It is given as,
V1 + V2 + V3 + V4 = 0
$\sum$ V = 0

Kirchhoff's Current Law

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Kirchhoff's Current Law (KCL) states that "The sum of the currents flowing into a junction is equal to the sum of the currents flowing out of the junction. In sum words, the algebraic sum of current at a node in the circuit is zero".

Look at the below circuit
Kirchhoff Current Law
By KCL, we have
$i_{1}$ + $i_{2}$ + $i_{4}$ = $i_{3}$ + $i_{5}$

Electric charge is never accumulated at any point in a circuit .The algebraic sum of electric currents at a junction in a circuit is zero .
$i_{1}$ + $i_{2}$ - $i_{3}$ + $i_{4}$ - $i_{5}$ = 0
This is known as Kirchhoff's Current law.

Electric Circuit Problems

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Lets go through same samples problems:

Solved Examples

Question 1: A 10 $\Omega$ resistor is connected across 10 V battery. Calculate the amount of current flowing through it.
Solution:
 
Given:
Resistance R = 10 $\Omega$, Voltage V = 10 V

Current I = $\frac{V}{R}$
             = $\frac{10\ v}{10\ \Omega}$
             = 1 A

 

Question 2: Calculate resistance R for the circuit
Electric Circuit Problem

Solution:
 
Resistance R = $\frac{4 \times 15}{4 + 15}$ $\Omega$ + (6 + 4) $\Omega$
                    = 3.157$\Omega$ + 10 $\Omega$
                    = 13.157 $\Omega$.