An electric circuit refers to a closed-loop via which a current can flow. Furthermore, the amount of current (amps) a circuit carries is dependent on the power and number of electrical devices whose connection is to the circuit. Also, electric circuit examples are direct-current circuit, alternating-current, series circuit, and parallel circuit.

**Introduction to Electric Circuit**

An electric circuit refers to a path for the transmitting of electric current. Furthermore, an electric circuit consists of a device that provides energy to the charged particles that constitute the current, for example, a generator or a battery, computers, lamps, electric motors etc.

There are two basic laws which mathematically explain the performance of electric circuits. Moreover, these laws are Kirchhoff’s rules and Ohm’s law. Also, the two types of electric circuits are series and parallel circuits.

**How do we Measure Electric Circuit?**

For beginners, the simple circuits that involve only a few components are usually easy and not complicated to understand. However, things become more complicated when other components come to the party.

The main questions that need to be asked here are- Where will the current go? What would the voltage do? Can simplification take place for easier understanding?

The first thing whose discussion must take place is the difference between parallel circuits and series circuits, by making use of the circuits involving the most basic of components – batteries and resistors. This would certainly bring out the difference between the two configurations. Afterwards, exploration must take place regarding what happens in series and parallel circuits on the combination of different types of components, for example, the inductors and capacitors.

A series circuit is a circuit in which the arrangement of the resistors takes place in a chain, so the current will have to take only one path. Furthermore, the current happens to be the same through each resistor. Also, one can find out the total resistance of the circuit by adding up the individual resistor’s resistance values.

A parallel circuit refers to a circuit in which the arrangement of the resistors takes place with their tails connected together, and their heads connected together. Furthermore, one can find out the total resistance of a set of resistors in parallel by adding up the reciprocals of the resistance values. Afterwards, one must take the reciprocal of the total.

**Formula of Electric Circuit**

Formula of series circuit is: R_{eq} = R1 + R2 + R3 +….

Moreover, formula of parallel circuit is: 1/R_{eq} = 1/R1 + 1/R2 + 1/R3 +….

Where,

R_{eq} = the total resistance of the resistors that are placed in series

R1, R2 … = resistors that are placed in series

**Derivation of the Formula of Electric Circuit**

**For Series Resistors:**

When the connection of a single resistor takes place in a circuit with a voltage source V, the current I via the circuit is given by Ohm’s Law:

I = V / R ……….. Ohm’s Law

Now let’s see what happens when we add a second resistor in series. Furthermore, series means that the resistors act like chain links, one after another. Moreover, we can call them as resistors R_{1} and R_{2}.

Due to the linking of the resistors together, the voltage source V causes the flowing of the same current I through both of them.

From Ohm’s Law, we have come to know that for a circuit with a resistance R and voltage V:

I = V / R

Therefore, facilitating a rearrangement of the equation by multiplying both sides by R

V = IR

So for resistor R_{1}

V_{1} = IR_{1}

and for resistor R_{2}

V_{2} = IR_{2}

V – V_{1 }– V_{2} = 0

Carrying out rearrangement

V = V_{1} + V_{2}

Furthermore, substituting for V_{1 }and V_{2} calculated earlier

V = IR_{1} + IR_{2} which is = I(R_{1} + R_{2})

Dividing both sides by I

V / I = R_{1} + R_{2}

However, from Ohm’s Law, we have come to know that V / I = total resistance of the circuit. Furthermore, let us call it R_{total}

Therefore,

R_{total} = R_{1} + R_{2}

Moreover, R_{total} = R_{1} + R_{2} + …… R_{n}

So, one must add up all the values in order to get the total resistance of resistors connected in series.

**For Parallel resistors:**

Each resistor that exists in the circuit has the full voltage. According to Ohm’s law, the currents that flow via the individual resistors are I_{1} = V/R_{2}, I_{2 }= V/R_{2}, and I_{3 }= V/R_{3}. Furthermore, conservation of charge implies that the total current happens to be the sum of these currents.

I= I_{1} + I_{2} + I_{3}.

Carrying out a substitution of the expressions for individual currents gives:

I = V/R_{1} + V/R_{2} + V/R_{3}

Or

I = V (1/R_{1} + 1/R_{2} + 1/R_{3})

This implies that a parallel circuit’s total resistance is equal to the sum of the inverse of each individual resistance. Therefore, for every circuit that has n number of resistors that have a connection in parallel,

R_{n} = 1/R_{1} + 1/R_{2} + 1/R_{3}…..+ 1/R_{n.}

**FAQs for Electric Circuit**

**Question 1: What is meant by electric circuit?**

**Answer 1:** An electric circuit refers to a closed-loop which facilitates the flowing of a current. Furthermore, an electric circuit refers to a path that facilitates the transmission of electric current.

**Question 2: Five 10k resistors and two 100k resistors are connected in series. What is the combined resistance?**

**Answer 2:** Resistor values are often specified in megaohms (abbreviated to “M”) or kiloohm (abbreviated to “k”).

1 kiloohm or 1k = 1000 ohms or 1 x 10^{3}

1 megaohm or 1M = 1000,000 ohms or in other words 1 x 10^{6}

To further simplify the arithmetic involved, it would be better if the values are written in scientific notation.

So for a series circuit:

Total resistance = sum of the resistances

= 5 x (10k) + 2 x (100k)

= 5 x ( 10 x 10^{3}) + 2 x (100 x 10^{3})

= 50 x 10^{3} + 200 x 10^{3}

= 250 x 10^{3 }or 250k

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