When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R , the rate of heat produced in R is J 1 . When the same batteries are connected in parallel ac

Question

When two identical batteries of internal resistance 1Ω each are connected in series across a resistor R , the rate of heat produced in R is J 1 ​ . When the same batteries are connected in parallel across R , the rate is J 2 ​ . If J 1 ​ = 2.25 J 2 ​ then the value of R in Ω is

TestHub · Accepted Answer

In series, i = 2 + R 2 E ​ ∴ J 1 ​ = i 2 R = ( 2 + R 2 E ​ ) 2 ⋅ R In parallel, i = 0.5 + R E ​ ∴ J 2 ​ J 2 ​ J 1 ​ ​ ​ = i 2 R = ( 0.5 + R E ​ ) 2 ⋅ R = 2.25 = ( 2 + R ) 2 4 ( 0.5 + R ) 2 ​ ​ or 1.5 = ( 2 + R ) 2 ( 0.5 + R ) ​ Solving we get, R = 4Ω ∴ The answer is 4 .

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