KCET · Physics · Current Electricity
A battery of emf \(E\) has an internal resistance r. A variable resistance \(R\) is connected to the terminals of the battery. A current \(i\) is drawn from the battery. \(V\) is the terminal potential difference. If \(R\) alone is gradually reduced to zero, which of the following best describes \(i\) and \(V\) ?
- A i approaches zero, \(V\) approaches E
- B \(i\) approaches \(\frac{E}{r}, V\) approaches zero
- C \(\mathrm{i}\) approaches \(\frac{\mathrm{E}}{\mathrm{r}}, \mathrm{V}\) approaches \(\mathrm{E}\)
- D i approaches infinity, \(V\) approaches \(E\)
Answer & Solution
Correct Answer
(B) \(i\) approaches \(\frac{E}{r}, V\) approaches zero
Step-by-step Solution
Detailed explanation
Current, \(\mathrm{i}=\frac{\mathrm{E}}{\mathrm{R}+\mathrm{r}}\) when \(\mathrm{R}\) decreases to \(0, \mathrm{i}=\frac{\mathrm{E}}{\mathrm{r}}\)
Similarly, potential difference \(V=i R\) when \(R\) decreases to \(0, \mathrm{~V}=0\)
Similarly, potential difference \(V=i R\) when \(R\) decreases to \(0, \mathrm{~V}=0\)
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