Combination of Resistors

 The combination of resistors occurs in two ways : 

• Resistors in Series
• Resistors in Parallel

Let’s discuss these in detail.

Resistors in Series

 If we want to raise overall resistance, we connect the individual resistances in series

Any number of resistances connected in series have a combined resistance that is equal to the sum of the individual resistances. As an illustration, the total resistance R is calculated as follows if several resistances R₁, R₂, R₃,… etc. are connected in series:

R = R₁ + R₂ + R₃ +…… 

Example: A resistance of 6 ohms is connected in series with another resistance of 4 ohms. A potential difference of 20 volts is applied across the combination. Calculate the current through the circuit.

 Solution:

 

Total resistance,

R = R₁ + R₂

R = 6 + 4

R = 10 ohms

Now, Total resistance, R = 10 ohms

Potential difference, V = 20 volts

and, Current in the circuit, I = ? (To be calculated)

So, applying Ohm’s law to the whole circuit, we get : 

V / I = R

20 / I = 10

I = 2 amperes

Thus, the current flowing through the circuit is 2 amperes.

Resistors in Parallel

if we want to decrease overall resistance, we connect the individual resistances in parallel.

The sum of the reciprocals of all the individual resistances is equal to the reciprocal of the combined resistance of a number of resistances connected in parallel.
For instance, the formula yields the total resistance R if a series of resistances, R₁, R₂, R₃, etc., are connected in parallel.

R = 1/R₁ + 1/R₂ + 1/R₃ + …

Example: Calculate the equivalent resistance when two resistances of 3 ohms and 6 ohms are connected in parallel.

Solution:

 

1/ R = 1 / R₁ + 1 / R₂

1 / R = 1 / 3 + 1 / 6

1 / R = (2+1) / 6

1 / R = 3 / 6

R = 2 ohm

NCERT Notes for Class 10 Physics Chapter 12 Electricity is important to study this chapter carefully because it forms the foundation for many other concepts that you will learn later on. Many exam questions will be based on this chapter, so it is essential to have a good understanding of the material.

Chapter 12 of the NCERT Class 10 Physics textbook explores electricity. It covers a variety of topics, including electric current, circuits, power, resistance in series and parallel, and Ohm’s Law. These notes are designed to provide students with a comprehensive summary of the entire chapter and include all of the essential topics, formulas, and concepts necessary for success on exams.