Electricity

Resistors connected in parallel circuit

Similar to other electrical components, when negative poles of more than one resistor are connected with negative terminal of electric circuit, and positive poles of the resistors are connected with positive terminal of the electric circuit, resistors connected is called resistors in parallel circuit.

Total Effective resistance of the circuit when resistors connected in parallel circuit

According to Law of combination of resistors in parallel the reciprocal of total effective resistance of the circuit is equal to the sum of reciprocal of resistances of individual resistor.

In the given figure, three resistors are connected in parallel:

Ref: Figure taken from NCERT book

Let there are three resistors R₁, R₂ and R₃ are connected in parallel in electric circuit.

Let the total effective resistance across the two ends of circuit = R

Therefore, according to Law of combination of resistors in parallel

Proof of Law of combination of resistors in parallel

Let,

The potential difference across the circuit is V.

The electric current across the end point of the circuit is I.

Electric current flows through R₁ = I₁

Electric current flows through R₂ = I₂

Electric current flows through R₃ = I₃

Since there is no division in potential difference taking place among the resistors connected in parallel circuit, hence potential difference through each of the resistors is equal to the potential difference across the two ends of circuit, i.e. equal to V.

According to Ohm's Law

Since, when more than one resistor is connected in parallel; the amount of total electric current flows through the circuit is equal to the sum of current flowing through each of the resistor.

After substituting the value of I in Ohm's Law from above equation we get

Thus, the reciprocal of resistance across the two ends of electric circuit is equal to the sum of reciprocal of resistance of each resistors connected in parallel circuit.

Similarly, if R₁, R₂, R₃, ……….. R_n resistances are connected in parallel in electric circuit. Then reciprocal total effective resistance, R across the end points of the circuit will be equal to the sum of reciprocal of resistance of all resistors.

Advantage and disadvantage of series circuit and parallel circuit

Series circuit

Advantage

Using series circuit high potential difference can be distributed to many electrical appliances; which work on low potential difference; without damaging them.

Example: 'Fairy lights' is used in decoration of buildings on many festive occasions or marriage ceremony. In 'fairy lights' many small bulbs, which work on very low potential difference (voltage), are connected in series and connected directly to the main line of households.

Electric line supplied in our house holds work between 220 V to 240 V. By connecting small bulbs of low potential difference in series this potential difference is distributed among them and 'fairy lights' work properly.

Example: Often electric call bell gets burnt because of frequent use, so to prevent electric calling from getting burnt, a bulb is connected in series so that potential difference distributed between electric bell and bulb.

Disadvantage

(a) If any one of the appliances connected in series circuit stops working, then all the appliances stop working because of break in electric circuit.

In such case it becomes very difficult to find out the defective piece.

You might have seen electrician spending lot of time in locating and replacing the dead bulb in fairy lights. Electrician has to test all of the bulbs one by one to find out dead one.

When too many appliances are connected in series and any one of them stops working, all others would stop working. Finding the defective appliance; like a fused bulb; in that case becomes a difficult task.

(b) There is only one switch to put off or on in appliances connected in series. Because of this one electrical appliance cannot be switched on or off as per requirement.

Parallel circuit

Advantage

(a) All appliances connected in parallel series work properly because potential difference is not divided in parallel connection, thus

(b) In the case of defect in any one of the appliances connected in parallel circuit, there is no effect on working on other appliances.

(c) All individual appliance connected in series can have individual switches, so any one of the appliances can be switched off as required.

(d) The total effective resistance gets reduced this makes the electric current high, because of this all appliances connected in parallel work properly and consume less electricity.

Disadvantage

(a) In parallel connection low voltage electrical appliance cannot be connected, otherwise they would be damaged.

Thus, parallel connection is suitable for household while series connection is suitable for connecting many appliances which work on low potential difference.