When comparing two circuits, you note that circuit one has twice the resistance and double the voltage of circuit two. this means that?

This means that there is same current flow in both the circuit, or the circuit one has twice the power of circuit two.

According to ohm's law, the resistance is given as

I=V/R

Since the circuit one has twice the voltage, and resistance

I1=I2

Current through any circuit = (voltage) / (resistance)

If both the voltage and the resistance are doubled, then the new current is

(2·V) / (2·R) = V/R

We can see that the current is the same in both circuits.

adding a(n) to an electric circuit would increase the magnetic field around a wire;

b. solenoid

a solenoid is a type of electromagnet whose purpose is to generate a controlled magnetic field.

if the purpose of the solenoid is instead to impede changes in the electric current, a solenoid can be more specifically classified as an inductor rather than an electromagnet.