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GUJCET · Physics · Current Electricity
When two identical cells are connected either in series or in parallel across \(2 \Omega\) resistor they send the same current through it. The internal resistance of each cell is ________.
- A \(0.5 \Omega\)
- B \(1.5 \Omega\)
- C \(1 \Omega\)
- D \(2 \Omega\)
Answer & Solution
Correct Answer
(D) \(2 \Omega\)
Step-by-step Solution
Detailed explanation
(D)
for series connection
current flowing through circuit
\(\begin{array}{l} I _1=\frac{2 \varepsilon}{ R +2 r} \\ I _1=\frac{2 \varepsilon}{2+2 r}\end{array}\)
for parallel connection
current flowing through circuit
\(\begin{array}{l} I _2=\frac{\varepsilon}{ R +\frac{r}{2}} \\ I _2=\frac{\varepsilon}{2+\frac{r}{2}}=\frac{2 \varepsilon}{4+r}\end{array}\)
As current is same in both connection
\(I_1=I_2\)
\(\begin{aligned} \frac{2 \varepsilon}{2+2 r} & =\frac{2 \varepsilon}{4+r} \\ 4+r & =2+2 r \\ 2 & =r \\ r & =2 \Omega\end{aligned}\)
for series connection
current flowing through circuit
\(\begin{array}{l} I _1=\frac{2 \varepsilon}{ R +2 r} \\ I _1=\frac{2 \varepsilon}{2+2 r}\end{array}\)
for parallel connection
current flowing through circuit
\(\begin{array}{l} I _2=\frac{\varepsilon}{ R +\frac{r}{2}} \\ I _2=\frac{\varepsilon}{2+\frac{r}{2}}=\frac{2 \varepsilon}{4+r}\end{array}\)
As current is same in both connection
\(I_1=I_2\)
\(\begin{aligned} \frac{2 \varepsilon}{2+2 r} & =\frac{2 \varepsilon}{4+r} \\ 4+r & =2+2 r \\ 2 & =r \\ r & =2 \Omega\end{aligned}\)
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