Question

# A cell sends a current through a resistance R for time t. Now the same cell sends current through another resistance r for the same time. If same amount of heat is developed in both the resistance, then the internal resistance of cell is

A
(R+r)2
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B
(Rr)2
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C
(Rr)2
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D
(Rr)
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Solution

## The correct option is B √(Rr)Explanation:-Suppose the internal resistance of the cell is x and E.M.F is ESo, while current flow through R ohm, total resistance is (R+x)So, current(I) through R ohm is ER+xFor the second case, Similarly, Current(I) flowing is Er+xSo if heat generated is same for time tthen, We have,I21Rt=I22rt⇒E2R(R+x)2=E2r(r+x)2⇒R(r+x)2=r(R+x)2⇒Rr2+Rx2=rR2+rx2⇒Rr(r−R)=x2(r−R)⇒x=√Rr [For r≠R]Hence the correct option is D

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