JEE Mains · Physics · STD 12 - Current electricity
- JEE Mains 2025
- Medium
- MCQ
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.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) Statement-I is false but Statement-II is true
Step-by-step Solution
Detailed explanation
In parallel connections
\(\begin{aligned}
& \frac{1}{r_{\mathrm{eq}}}=\frac{1}{r_1}+\frac{1}{r_2} \\
& \frac{E_{\mathrm{eq}}}{r_{\mathrm{eq}}}=\frac{E_1}{r_1}+\frac{E_2}{r_2}
\end{aligned}\)
If \(E_1=E_2\) and \(r_1=r_2, E_{\text {eq }}=E_1=E_2\)
\(\therefore\) Statement 1 is false.
\(r_{\text {eq }}\) is less then both \(r_1\) and \(r_2\)
\(\therefore\) Statement II is true
\(\begin{aligned}
& \frac{1}{r_{\mathrm{eq}}}=\frac{1}{r_1}+\frac{1}{r_2} \\
& \frac{E_{\mathrm{eq}}}{r_{\mathrm{eq}}}=\frac{E_1}{r_1}+\frac{E_2}{r_2}
\end{aligned}\)
If \(E_1=E_2\) and \(r_1=r_2, E_{\text {eq }}=E_1=E_2\)
\(\therefore\) Statement 1 is false.
\(r_{\text {eq }}\) is less then both \(r_1\) and \(r_2\)
\(\therefore\) Statement II is true
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