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प्रश्न
First a set of n equal resistors of R each are connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current is increased 10 times. What is ‘n’?
उत्तर
The equivalent resistance of series combination is in series with the internal resistance R of battery and in parallel combination of resistors, the equivalent resistance of parallel combination is also in series with the internal resistance of battery.
In series combination of resistors, current I is given by `I = E/(R + nR)`
Whereas in parallel combination current 10I is given by `E/(R + R/n) = 10I`
Now, according to problem,
`(1 + n)/(1 + 1/n)` ⇒ `10 = ((1 + n)/(n + 1))n`
⇒ n = 10
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