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Q.

When a battery sends current through a resistance R1 for time ‘t’ , the heat produced in the resistor is Q. When the same battery sends current through another resistance R2 for time ‘t’ , the heat produced in R2 is again ‘Q’. The internal resistance of battery is

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a

R1+R22

b

R1- R22

c

R1R2

d

R1+R22

answer is C.

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Detailed Solution

Q=i12 R1t  = i22 R2t  ⇒Er + R12R1=Er + R22R2 ⇒Er + R1R1=Er + R2R2 ⇒rR1 +R1.R2 =rR2 +R2.R1 ⇒rR1  -rR2 =R2.R1-R1.R2 ⇒rR1  -R2 =R2R12-R1R22 ⇒r = R1 R2 R1-R2R1-R2 ⇒r = R1R2
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When a battery sends current through a resistance R1 for time ‘t’ , the heat produced in the resistor is Q. When the same battery sends current through another resistance R2 for time ‘t’ , the heat produced in R2 is again ‘Q’. The internal resistance of battery is