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JEE Main 2014 · 9 Apr · Shift 1, Physics question 18

A d.c. main supply of e.m.f. 220 V is connected across a storage battery of e.m.f. 200 V through a resistance of 1 Ω. The battery terminals are connected to an external resistance 'R'. The minimum value of 'R', so that a current passes through the battery to charge it is :

Choose one option
Answer and worked solution

Official answer: C

The supply drives current through 1 Ω to the junction, held at 200 V by the battery. The current from the supply is 220−2001=20\frac{220-200}{1}=20 A; R takes 200R\frac{200}R. The battery charges only if
20−200R>0  ⟹  R>10 Ω.20-\frac{200}R>0\implies R>10\ \Omega.
Of the options, the smallest value that works is 11 Ω.

Topics:Kirchhoff's lawsEMF and internal resistance
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