A series combination of 10 capacitors, each of value ' C₁ ' is charged by a source of potential difference ' 4V '. When another parallel combination of 8 capacitors, each of value ' C₂ ' is charged by a source of potential difference ' V '. The relation between C₁ and C₂ , so that the energies in the two combinations will be same is

Step-by-step solution

For the series combination of 10 capacitors, each of capacitance C₁ : Equivalent capacitance, C_ eq1 = C₁ 10 Potential difference, V₁ = 4V Energy stored, U₁ = 1 2 C_ eq1 V₁^2 = 1 2 ( C₁ 10 ) (4V)^2 = 16 C₁ V^2 20 = 4 5 C₁ V^2 For the parallel combination of 8 capacitors, each of capacitance C₂ : Equivalent capacitance, C_ eq2 = 8 C₂ Potential difference, V₂ = V Energy stored, U₂ = 1 2 C_ eq2 V₂^2 = 1 2 (8 C₂) V^2 = 4 C₂ V^2 Given that the energies in the two combinations are the same ( U₁ = U₂ ): 4 5 C₁ V^2 = 4 C₂