Devices in Series and Parallel

Concept Explanation

Devices in Series and Parallel

Sometimes we come across a circuit which consists of more than one type of combination of resistance. That means some resistance may be parallel to each other and this combination can be in series with another resistance. Or we have different parallel combinations of resistance which are in series to each other. A combination circuit has some resistances connected in series combination and some parallel combination.

This type of combination is also called complex circuit. While solving problems of mixed combination of resistances, there are many points to be considered as given below:

The first step is to reduce the mixed combination of resistance into a simple circuit containing only one resistor. For this examine, the given circuit and replace the resistors that are connected in parallel or in series with their equivalent resistances.

Draw the new circuit after making the changes and repeat the same procedure again and again till a simple circuit is obtained.

If the current through or potential difference across a resistor in the complex circuit is to be found, then start with the simple circuit reduced from the complex circuit and gradually work your way back through the circuits, using V= IR.

While calculating the equivalent resistance, do not consider the battery as we consider that the battery has negligible resistance. But, if its resistance is given, then consider it as an individual resistor.

Illustration: Consider the circuit diagram as shown in the figure

$large If ;R_{1}=R_{2}=R_{3}=R_{4}=R_{5}=3Omega$

then find the equivalent resistance of the circuit.

Solution: From the combination, it can be observed that $dpi{100} large R_{2};and;R_{3}$ are connected in series order. As current through $large R_{2};and;R_{3}$ is same. So, their equivalent resistance is

$R^i=R_{2}+R_{3}=3Omega +3Omega =6Omega$

Now, the given circuit can be redrawn as shown in the figure

Now, it can be seen that $large R_{4};and;R^i$ are in parallel combination. As, currents through $large R_{4};and;R^i$ are different. So, their equivalent resistance can be calculated as below

$frac{1}{R^{ii}}= frac{1}{R_4}+ frac{1}{R^{i}}=frac{1}{3}+frac{1}{6}=frac{2+1}{6}=frac{3}{6}=frac{1}{2}$

$therefore ;R^{ii}=2;Omega$

Now, the given circuit can be redrawn as shown in the figure

Now, it is clear from the diagram that all the resistances $large R_{5},R^{ii};and;R_{1}$ are in series combination.

As, current through $large R_{1},R^{ii};and;R_{5}$ is same.

$large therefore$ Equivalent resistance of the circuit is

$large R=R_{5}+R^{ii}+R_{1}=3Omega +2Omega +3Omega =8Omega$

The battery has potential as = 16 V

By using the formula V = IR

$I=frac{V}{R}= frac{16}{8}= 2 A$

As current flowing through $large R_{1},R^{ii};and;R_{5}$ is same because they are in series. So

$I_1= 2 A;,;I^{ii}= 2 A; and; I_5= 2 A$ and potential drop across them is

$V_1= 2; X ;3= 6;V ;,;V^{ii}= 2; X; 2= 4;V; and; V_5= 2; X;3= 6; V$

As $R^{ii}$ is an equivalent resistance for a parallel combination of $large R_{4};and;R^i$ , So potential drop across them is the same

$I_4= frac{V_4}{R_4}=frac{4}{3}=1.33;A; and; I^i= frac{V^i}{R^i}=frac{4}{6}=0.67;A$

As $R^i$ is an equivalent resistance for a series combination of $large R_{2};and;R_3$ , So current flowing through is the same i.e 0.67 A

$V_2= frac{2}{3}; X ;3= 2;V; and; V_3= frac{2}{3}; X;3= 2; V$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

In our houses all electrical devices operate on 220 V. It implies that-
A. they are connected in parallel	B. they are connected in series	C. they all have currents of equal values	D. they all have the same resistance
Right Option : A
View Explanation

Question : 2

In a circuit if two resistance of 3ohms each are connected in parralel and then connected in series with another combination of two resistance of 2 ohms which are connected in parallel then what is the net resistance of the circuit
A. 10 ohms	B. 2/5 ohms	C. 5/2 ohms	D. none of these
Right Option : C
View Explanation

Question : 3

Marie conducted an experiment to find out if the number of bulbs arranged in series would affect the brightness of the bulbs. which of the following variables should be kept the same? A. Type of bulbs B. number of wires C. Types of batteries D. number of bulbs
A. D only	B. B and D only	C. A,B and C only	D. A,B,C and D
Right Option : C
View Explanation

Students / Parents Reviews [20]

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.

Eshan Arora

8th

My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak poi...

Shivam Rana

7th

The experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confi...

Aman Kumar Shrivastava

10th

Abhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of per...

Yogansh Nyasi

7th

My experience with Abhyas Academy has been very good. When I was not in Abhyas whenever teacher ask questions I could not speak it confidently but when I came in Abhyas, my speaking skills develope...

Upmanyu Sharma

7th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

In terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...

Aman Kumar Shrivastava

10th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...

Aman Kumar Shrivastava

10th

Usually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...

Anika Saxena

8th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has...

Shreya Shrivastava

8th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

We started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.

Manya

8th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are v...

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...

Shreya Shrivastava

8th

Abhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary ...

Manish Kumar

10th

My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.

Hiya Gupta

8th

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.

Ayan Ghosh

8th

View All

Attention !!!!!

Devices in Series and Parallel

Devices in Series and Parallel

Students / Parents Reviews [20]

Cheshta

Eshan Arora

Shivam Rana

Aman Kumar Shrivastava

Yogansh Nyasi

Upmanyu Sharma

Yatharthi Sharma

Aman Kumar Shrivastava

Aman Kumar Shrivastava

Aman Kumar Shrivastava

Anika Saxena

Barkha Arora

Shreya Shrivastava

Manish Kumar

Manya

Shreya Shrivastava

Manish Kumar

Hiya Gupta

Archit Segal

Ayan Ghosh