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Question

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 h fraction of total electrical power generated in it.; then which of the following graph is correct

  1.    
  2.    
  3.    
  4. Both (a) and (b) are correct    

The correct answer is: Both (a) and (b) are correct


    Terminal voltage V equals E minus 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 equals E I minus I to the power of 2 end exponent 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 to the power of 2 end exponent r and total electrical power generated in the cell = Ei. Hence the fraction eta equals fraction numerator I to the power of 2 end exponent r over denominator E I end fraction equals open parentheses fraction numerator r over denominator E end fraction close parentheses I semicolon so eta proportional to I. It means graph between h and I will be a straight line passing through origin.

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