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

A 24V potential difference is applied across a parallel combination of four 6ohm resistor.The current in each resistor is-
A. 1A	B. 4A	C. 16A	D. 36A
Right Option : B
View Explanation

Question : 2

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 : 3

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

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Devices in Series and Parallel

Devices in Series and Parallel

Students / Parents Reviews [10]

Manish Kumar

Eshan Arora

Hiya Gupta

Yatharthi Sharma

Archit Segal

Barkha Arora

Shivam Rana

Prisha Gupta

Aman Kumar Shrivastava

Cheshta