Two ideal capacitors C₁ and C₂ are connected to two different AC sources. The first circuit has capacitance C₁ = C , rms voltage V₁ = V , and frequency f₁ = f . The second circuit has capacitance C₂ = C 2 , rms voltage V₂ = 2V , and frequency f₂ = 2f . The ratio of the rms currents I₁ : I₂ in the two circuits is:

Step-by-step solution

The rms current in a purely capacitive circuit is given by I = V X_C . Since X_C = 1 2 f C , the current can be written as I = V(2 f C) . For the first circuit: I₁ = V(2 f C) For the second circuit: I₂ = (2V)(2 2f C 2 ) = 2V(2 f C) = 2I₁ Therefore, the ratio of the rms currents is I₁ : I₂ = 1 : 2 . Answer: 1 : 2