Question

Given below are two statements :

Statement-I: The equivalent emf of two non-ideal batteries connected in parallel is smaller than either of the two emfs.

Statement-II: The equivalent internal resistance of two non-ideal 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:

(1) Statement-I is true but Statement-II is false

(2) Both Statement-I and Statement-II are false

(3) Both Statement-I and Statement-II are true

(4) Statement-I is false but Statement-II is true

Answer 1

Correct option is: (4) Statement-I is false but Statement-II is true

\(\varepsilon_{eq} = \frac{\varepsilon_1 r_2 + \varepsilon_2 r_1}{r_1 + r_2}\)

check for \(r_1 = r_2 \Rightarrow \varepsilon_{eq} = \frac{\varepsilon_1 + \varepsilon_2}{2}\)

So S1 is false

S2 \(: r_{eq} = \frac{r_1 r_2}{r_1 + r_2} < r_1 \ \text{or} \ r_2\)

S2 is true