Question 138: Current Electricity

Question

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.

Accepted Answer

When two non-ideal batteries are connected in parallel, their equivalent emf is
$${E_{eq}} = {{{{{E_1}} \over {{r_1}}} + {{{E_2}} \over {{r_2}}}} \over {{1 \over {{r_1}}} + {1 \over {{r_2}}}}} \Rightarrow {E_{eq}} = {{{E_1}{r_2} + {E_2}{r_1}} \over {{r_1} + {r_2}}}$$
If emf of both cells is same say E,
$${E_{eq}} = {{E{r_2} + E{r_1}} \over {{r_1} + {r_2}}} = {{E({r_1} + {r_2})} \over {({r_1} + {r_2})}} = E$$
Hence, equivalent emf is equal to emf of the single cell.
Also, when two non-ideal batteries are connected in parallel, their equivalent resistance is $${r_{eq}} = {{{r_1}{r_2}} \over {{r_1} + {r_2}}}$$
Hence, the equivalent internal resistance is smaller than either of the two internal resistances. Therefore 1 is correct.

Answer

Statement-I is false but Statement-II is true

Answer

Statement-I is true but Statement-II is false

Answer

Both Statement-I and Statement-II are false

Answer

Both Statement-I and Statement-II are true

Current Electricity

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