Q.

The series combination of two batteries both of the same emf 10 V ,  but different internal resistance of 20Ω and 5Ω  is connected to the parallel combination of two resistors 25Ω and R Ω .The voltage difference across the battery of internal resistance 20 Ω is zero . The value of Rin Ω is,

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answer is 0037.50.

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Detailed Solution

For 10 V, 20Ω battery : ∴  V1 = ε1−ir1 ⇒0=10−i×20 i=0.5A  For 10 V, 5Ω battery : ∴ V2 = ε2 −i r2 =10−0.5×5=7.5V  The potential difference across all three branches is equal. V = V1 + V2  = 0 + 7.5 = 7.5 V  Now, i = i1 + i2 ⇒0.5 = 7.525 +7.5R ⇒0.5=0.3+7.5R ⇒0.2=7.5R ⇒R = 7.50.2=37.5 Ω
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The series combination of two batteries both of the same emf 10 V ,  but different internal resistance of 20Ω and 5Ω  is connected to the parallel combination of two resistors 25Ω and R Ω .The voltage difference across the battery of internal resistance 20 Ω is zero . The value of Rin Ω is,