Two sources of equal emf are connected to an external resistance R. The internal resistances of the two sources are R₁ and R₂ (R₂ > R₁). If the potential difference across the source having internal resistance R₂ is zero, then (a) R = R₂ - R₁ (b) R = R₂ × (R₁ + R₂)/(R₂ - R₁) (c) R = R₁ R₂/(R₂ - R₁) (d) R = R₁R₂/(R₁ - R₂)

Answer: (a). Sources in series: I = (2E)/(R + R₁ + R₂). P.d. across source R₂ is zero: E - IR₂ = 0 ⇒ I = E/R₂. 2R₂ = R + R₁ + R₂ So the answer is (a) R = R₂ - R₁.

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Cells: EMF, Internal Resistance & Combinations

Two sources of equal $\text{emf}$ are connected to an external resistance $R.$ The internal resistances of the two sources are $R_1$ and $R_2\ (R_2 > R_1).$ If the potential difference across the source having internal resistance $R_2$ is zero, then

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Answer: (a)

Sources in series: $I = \dfrac{2E}{R + R_1 + R_2}$ .
P.d. across source $R_2$ is zero: $E - IR_2 = 0 \Rightarrow I = \dfrac{E}{R_2}$ .
$2R_2 = R + R_1 + R_2$
So the answer is (a) $R = R_2 - R_1$ .

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