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Standard XII

Physics

Symmetry in Circuits

Find the emf ...

Question

Find the emf and internal resistance of a single battery which is equivalent to a combination of three batteries as shown in the figure.

$3 V, 5 Ω$

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$3 V, 2 Ω$

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$7 V, 2 Ω$

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$20 V, 5 Ω$

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Solution

The correct option is B
$3 V, 2 Ω$

Equivalent internal resistance, $r_{e f f} = 1 + (2 | | 2) = 1 + \frac{2 \times 2}{2 + 2} = 1 + 1 = 2 Ω$
Equivalent emf, $E_{e f f} = E_{3} - \frac{E_{1} r_{2} - E_{2} r_{1}}{r_{1} + r_{2}} = 6 - (\frac{10 \times 2 - 4 \times 2}{2 + 2}) = 6 - \frac{12}{4} = 3 V$

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(IIT-JEE 1997)

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Find the emf and internal resistance of a single battery which is equivalent to a combination of three batteries as shown in the figure.

The correct option is B 3 V,2 Ω Equivalent internal resistance, reff=1+(2||2)=1+2×22+2=1+1=2 Ω Equivalent emf, Eeff=E3−E1r2−E2r1r1+r2=6−(10×2−4×22+2)=6−124=3 V