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Cells, emf, Internal Resistance

Battery shown in figure has e.m.f. E and internal resistance r

Question

Medium

Solving time: 3 mins

Battery shown in figure has e.m.f. $E$ and internal resistance $r$ . Current in the circuit can be varied by sliding the contact $J$ . If at any instant current flowing through the circuit is $I$ , potential difference between terminals of the cell is $V$ , thermal power generated in the cell is equal to $η$ fraction of total electrical power generated in it; then which of the following graphs is correct?

Both (a) and (b) are correct

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Asher Discussed

Battery shown in figure has e.m.f.

E

and internal resistance

r

. Current in the circuit can be varied by sliding the contact

J

. If at any instant current flowing through the circuit is

I

, potential difference between terminals of the cell is

V

, thermal power generated in the cell is equal to

η

fraction of total electrical power generated in it; then which of the following graphs is correct?

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Terminal voltage,

V = E - I r

. Hence the graph between

V

and

i

will be a straight line having negative slope and positive intercept.
Thermal power generated in the external circuit

P = E I - I^{2} r

. Hence graph between

P

and

I

will be a parabola passing through origin.
Also at an instant, thermal power generated in the cell

= i^{2} r

and total electrical power generated in the cell

= E i

. Hence the fraction

η = \frac{I ^{2} r}{E I} = (\frac{r}{E}) I

; so

η \propto I

. It means graph between

η

and

I

will be a straight line passing through origin.

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Question Text	Battery shown in figure has e.m.f. $E$ and internal resistance $r$ . Current in the circuit can be varied by sliding the contact $J$ . If at any instant current flowing through the circuit is $I$ , potential difference between terminals of the cell is $V$ , thermal power generated in the cell is equal to $η$ fraction of total electrical power generated in it; then which of the following graphs is correct?
Topic	Current Electricity
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	69

Text solutionVerified

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