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Question

For the batteries shown in the figure, R1,R2, and R3 are the internal resistances of E1,E2, and E3 respectively. Then, which of the following is/are correct?


A
The equivalent internal resistance R of the system is given by (R1R2R3)(R1R2+R2R3+R3R1).
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B
If E3=(E1R2+E2R1)(R1+R2), the equivalent emf of the batteries will be equal to E3.
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C
The equivalent e.m.f. of the battery is equal to
=E1+E2+E33
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D
The equivalent e.m.f. of the battery not only depends upon values of E1,E2 and E3 but also depends upon values of R1,R2 and R3.
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Solution

The correct option is D The equivalent e.m.f. of the battery not only depends upon values of E1,E2 and E3 but also depends upon values of R1,R2 and R3.
The equivalent internal resistance diagram of the circuit can be shown as
Equivalent internal resistance is given by
1R=1R1+1R2+1R3
1R=R1R2+R2R3+R3R1R1R2R3

R=R1R2R3R1R2+R2R3+R3R1

According to question, we need to take
Eeq=E3
Eeq=ER1R=E1R1+E2R2+E3R31R1+1R2+1R3---(i)
E3=E1R1+E2R2+E3R31R1+1R2+1R3

E3R1+E3R2+E3R3=E1R1+E2R2+E3R3

E3=E1R2+E2R1R1+R2

From equation (i) we can say that the equivalent emf of the battery depends not only on values of E1,E2 and E3 but also depends on values of R1, R2 and R3.

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