Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Two cell emf and internal resistance  and 

Two cell emf and internal resistance \varepsilon _{1}, r_{1} and \varepsilon _{2}, r_{2} are connected in parallel. Derive the expressions for the emf and internal resistance of a cell which can replace this combination.

 

Answers (1)

Emf are \varepsilon _{1}and \varepsilon _{2}

Internal resistance are r _{1}andr _{2}

Here, I=I _{1}+I_{2}            ........(1)

Let V is the potential differnace between B1 and B2

Then V = \varepsilon _{1}-I_{1}r_{1}

Therefore , I_{1}= \frac{\varepsilon _{1}-V}{r_{1}}                ......(2)

Similarly. I_{2}= \frac{\varepsilon _{2}-V}{r_{2}}                   .......(3)

Putting equation (2) and (3) in (1)

I=\frac{\varepsilon _{1}-V}{r_{1}}+ \frac{\varepsilon _{2}-V}{r_{2}}

 I=\left ( \frac{\varepsilon _{1}}{r_{1}}+\frac{\varepsilon _{2} }{r_{2}} \right )-V\left ( \frac{1}{r_{1}}+\frac{1}{r_{2}} \right )

or V = \left ( \frac{\varepsilon _{1}r_{2}+\varepsilon _{2}r_{1}}{r_{1}+r_{2}} \right )- I\left ( \frac{r_{1}r_{2}}{r_{1}+r_{2}} \right )

If we replace this with a single cell it can be written as 

V = \varepsilon _{equivalent}-Ir_{eqivalent}

Then, 

\varepsilon _{eqivalent} = \left ( \frac{\varepsilon _{1}r_{2}+\varepsilon _{2}r_{1}}{r_{1}+r_{2}} \right )

r_{equivalent} =\left ( \frac{r_{1}r_{2}}{r_{1}+r_{2}} \right )

Posted by

Safeer PP

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question