Two cells of emf 6 V and 3 V and internal resistances 2 and 1 , respectively, are connected in series (assisting each other) with an external resistance R . The total current in the circuit is I_s . Now, the same two cells are connected in parallel (similar poles connected together) across the same external resistance R . In this case, the total current drawn is I_p . If the ratio I_s I_p = 2 , the value of R in is _

Step-by-step solution

For the series combination, the equivalent emf and internal resistance are: _s = ₁ + ₂ = 6 + 3 = 9 V r_s = r₁ + r₂ = 2 + 1 = 3 The current in the series circuit is: I_s = _s R + r_s = 9 R + 3 For the parallel combination, the equivalent emf and internal resistance are: _p = ₁ r₁ + ₂ r₂ 1 r₁ + 1 r₂ = 6 2 + 3 1 1 2 + 1 1 = 3 + 3 3 2 = 4 V r_p = r₁ r₂ r₁ + r₂ = 2 1 2 + 1 = 2 3 The current in the parallel circuit is: I_p = _p R + r_p = 4 R + 2 3 Given that I_s I_p = 2 , we have: 9 R + 3 4 R + 2 3 = 2 9 R + 3 = 8 R + 2