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QJEEM23Ph0fc2: JEE Main 2023 Physics - Class 12 JEEM23Ph0fc2 Solution: Two identical cells, when connected either in parallel or in…

Two identical cells, when connected either in parallel or in series gives same current in an external resistance 5 Ω5 ~\Omega . The internal resistance of each cell will be ___________ Ω\Omega .

Step-by-Step Verified Solution

JEE Main 2023 (Online) 31st January Morning Shift Physics - Current Electricity Question 101 English Explanation 1
εseries =ε1+ε2=2ε\varepsilon_{\text {series }}=\varepsilon_{1}+\varepsilon_{2}=2 \varepsilon

rseries =r1+r2=2rr_{\text {series }}=r_{1}+r_{2}=2 r

i=2ε5+2ri=\frac{2 \varepsilon}{5+2 r} ......(1) JEE Main 2023 (Online) 31st January Morning Shift Physics - Current Electricity Question 101 English Explanation 2
εparallel =ε1r1+ε2r21r1+1r2=ε\varepsilon_{\text {parallel }}=\frac{\frac{\varepsilon_{1}}{r_{1}}+\frac{\varepsilon_{2}}{r_{2}}}{\frac{1}{r_{1}}+\frac{1}{r_{2}}}=\varepsilon

rparallel =r2r_{\text {parallel }}=\frac{r}{2}

i=εr2+5i=\frac{\varepsilon}{\frac{r}{2}+5} .......(2)

Equating (1) and (2), we get

⇒2ε2r+5=εr2+5\Rightarrow \frac{2 \varepsilon}{2 r+5}=\frac{\varepsilon}{\frac{r}{2}+5}

⇒r+10=2r+5\Rightarrow r+10=2 r+5

⇒r=5Ω\Rightarrow r=5 \Omega

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