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Current Electricity

Question
CBSEENPH12039010

A cell of emf ‘E’ and internal resistance ‘r’ is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I.

It is found that when R = 4 straight capital omega, the current is 1 A and when R is increased to 9 straight capital omega , the current reduces to 0.5 A. Find the values of the emf E and internal resistance r.

Solution

Plot for V vs. R  

Plot for V vs. I

Current in the circuit is given by, 


straight I straight space equals straight space fraction numerator straight epsilon over denominator straight R plus straight space straight r end fraction

Terminal straight space voltage comma straight space straight V straight space equals straight space IR straight space equals straight space straight V subscript straight A minus straight space straight V subscript straight B

straight V straight space equals straight space fraction numerator εI over denominator straight R plus straight space straight r end fraction straight space equals straight epsilon straight space – straight space Ir

straight I straight space equals straight space fraction numerator straight epsilon over denominator 4 plus straight space straight r end fraction

rightwards double arrow straight space straight r straight space plus 4 straight space equals straight space straight epsilon straight space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... space left parenthesis 1 right parenthesis space

0.5 straight space equals straight space fraction numerator straight epsilon over denominator 9 plus straight space straight r end fraction

rightwards double arrow straight space 0.5 straight r straight space plus straight space 4.5 straight space equals straight space straight epsilon space space space space space space space space space space space space space space space space space space space space space space space space... space left parenthesis 2 right parenthesis thin space

On space solving space equations space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space have space space

Internal space resistance comma space straight r space equals space 1 space space comma space and space space

EMF comma space straight epsilon space space equals space 5 space Volt

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