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Define internal resistance of a cell. Pr...

Define internal resistance of a cell. Prove that `r ~= ((E)/(V) - 1)R`, where R is the external resistance used.

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(a) Two cells of emfe and € have their internal resistances epsi_(1) and epsi_(2) respectively. Deduce an expression for the equivalent emf and internal resistance of their parallel combination when connected across an external resistance R. Assume that the two cells are supporting each other. (b) In case the two cells are identical, each of emf e= 5V and internal resistance r= 2Omega, calculate the voltage across the external resistance R= 10Omega.

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Knowledge Check

  • In a closed circuit, the e.m.f. and internal resistance of the generator are E and r respectively. If the external resistance in the circuit is R, then Ohm's law has the form

    A
    `I=(E)/(Rr)`
    B
    `I=(E)/(R)`
    C
    `I=(E)/(r)`
    D
    `I=(E)/((R+r))`

  • Two cells of emf 3V and 5V and internal resistance r_(1) and r_(2) respectively are in series with an external resistance R. if the p.d. across 1 st cell is zero, then R is

    A
    `(5r_(1)-3r_(2))/(3)`
    B
    `(2r_(1)-3r_(2))/(4)`
    C
    `(3r_(1)-5r_(2))/(3)`
    D
    `(4r_(1)-5r_(2))/(3)`

  • Two cells of same emf epsilon but of different internal resistances r_1 and r_2 are connected in series with an external resistance R. The potential drop across the first cell is found to be zero. The external resistance R is

    A
    `r_1+r_2`
    B
    `r_1-r_2`
    C
    `r_2-r_1`
    D
    `r_1^2//r_2`

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