Hi, I've been asked by mother to help out one of her friends with a physics problem (she is doing a maths degree and got a physics question) however my knowledge of physics in this area appears to be even more limited. So if I write the problem out here could someone please point me in the right direction to give help.

I will write out everything I was given:

Presumably this is a multiple-choice question, any help would be great thanks.

Perhaps they're looking for the equivalent capacitance? If so, then capacitors in series (as these are) are equivalent to a single capacitor with capacitance C_{eq}=C_{1}C_{2}/(C_{1}+C_{2}).

The answer to the capacitor question has answers 2i=Cdv/dt

or

i = 2C dv/dt

but I am unsure as to the correct choice.

It should be borne in mind that this question is not really about physics but is rather about modelling physical networks and is taught in general terms where the same formulation is used for various branches of science.

So we are using Kirchoff's laws in general terms, given three sets of equations, component equations, vertex law equations and the cycle law equations.

Well, I am not sure about the terms used in the problem, but usually A, B, .... mean nodes in a electric circuit. You can imagine that the circuit in the figure is a part of a bigger net. The two capacitors are connected in parallel with respect to A and B. For parallel connected components, the voltages are the same. The voltage is the same across both capacitors V(AB)=V1=V2 and the current which flows through the single component between A and B is the sum of i1 and i2, i(AB) = i1 + i2. The component equation for a capacitor is Q=C*V, and i = dQ/dt=C*dV/dt--->i= i1+i2 = C1*dV/dt + C2*dV/dt = (C1+C2)*dV/dt = C(AB)*dV/dt for the single component capacitor between A and B. If both capacitances are equal i = 2C*dv/dt.