Class 10 Exam  >  Class 10 Questions  >  When two resistors of resistance R1 and R2 ar... Start Learning for Free
When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.?
Most Upvoted Answer
When two resistors of resistance R1 and R2 are connected in parallel, ...
Community Answer
When two resistors of resistance R1 and R2 are connected in parallel, ...
Given:

Resistance of first resistor, R1 = ?

Resistance of second resistor, R2 = ?

Net resistance in parallel, Rp = 3 Ω

Net resistance in series, Rs = 16 Ω


Solution:

Let's use the formulas for calculating the net resistance of resistors in parallel and series.


For parallel connection:

The net resistance for two resistors in parallel is given by:

1/Rp = 1/R1 + 1/R2

Substituting the given value of Rp as 3 Ω, we get:

1/3 = 1/R1 + 1/R2

Equation (1)


For series connection:

The net resistance for two resistors in series is given by:

Rs = R1 + R2

Substituting the given value of Rs as 16 Ω, we get:

16 = R1 + R2

Equation (2)


Solving the equations:

We have two equations (1) and (2) with two variables R1 and R2. We can solve these equations simultaneously to get the values of R1 and R2.

From equation (2), we can solve for R2:

R2 = 16 - R1

Substituting this value of R2 in equation (1), we get:

1/3 = 1/R1 + 1/(16 - R1)

Multiplying both sides by 48R1(16 - R1), we get:

16R1 - R1^2 = 48 + 3R1(16 - R1)

Simplifying and rearranging, we get a quadratic equation:

R1^2 - 13R1 + 48 = 0

Factoring the equation, we get:

(R1 - 8)(R1 - 5) = 0

So, the possible values of R1 are 8 Ω and 5 Ω.


Final answer:

Therefore, the values of R1 and R2 are:

R1 = 8 Ω and R2 = 16 - R1 = 8 Ω

OR

R1 = 5 Ω and R2 = 16 - R1 = 11 Ω

So, the two resistors can have values of 8 Ω and 8 Ω or 5 Ω and 11 Ω to satisfy the given conditions.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
Explore Courses for Class 10 exam

Top Courses for Class 10

When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.?
Question Description
When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.?.
Solutions for When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.? in English & in Hindi are available as part of our courses for Class 10. Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.? defined & explained in the simplest way possible. Besides giving the explanation of When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.?, a detailed solution for When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.? has been provided alongside types of When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.? theory, EduRev gives you an ample number of questions to practice When two resistors of resistance R1 and R2 are connected in parallel, the net resistance is 3ohm. When connected in series ,its value is 16 ohm. Calculate the value of R1 and R1.? tests, examples and also practice Class 10 tests.
Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev