Given below are two statements :
Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs.
Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries.
In the light of the above statements, choose the correct answer from the options given below.
Solution
<p>When two non-ideal batteries are connected in parallel, their equivalent emf is</p>
<p>$${E_{eq}} = {{{{{E_1}} \over {{r_1}}} + {{{E_2}} \over {{r_2}}}} \over {{1 \over {{r_1}}} + {1 \over {{r_2}}}}} \Rightarrow {E_{eq}} = {{{E_1}{r_2} + {E_2}{r_1}} \over {{r_1} + {r_2}}}$$</p>
<p>If emf of both cells is same say E,</p>
<p>$${E_{eq}} = {{E{r_2} + E{r_1}} \over {{r_1} + {r_2}}} = {{E({r_1} + {r_2})} \over {({r_1} + {r_2})}} = E$$</p>
<p>Hence, equivalent emf is equal to emf of the single cell.</p>
<p>Also, when two non-ideal batteries are connected in parallel, their equivalent resistance is ${r_{eq}} = {{{r_1}{r_2}} \over {{r_1} + {r_2}}}$</p>
<p>Hence, the equivalent internal resistance is smaller than either of the two internal resistances. Therefore 1 is correct.</p>
About this question
Subject: Physics · Chapter: Current Electricity · Topic: Ohm's Law and Resistance
This question is part of PrepWiser's free JEE Main question bank. 120 more solved questions on Current Electricity are available — start with the harder ones if your accuracy is >70%.