When two resistors are connected across the same two points in a circuit, they form a parallel circuit. In this arrangement, the voltage across each resistor is the same, and the current from the source splits between the two paths. This is what defines a parallel configuration, and it differs from a series circuit (where the same current flows through components laid end-to-end) and from a short circuit (which bypasses components with a very low-resistance path). A mixed circuit would combine both series and parallel portions, not be purely parallel.

The speed in question is about orders of magnitude larger than everyday motion—astronomical objects moving around the center of the Milky Way travel at speeds that are tens to hundreds of kilometers per second. In common quick estimates used for teaching, these galactic orbital speeds are often rounded to a value around 100,000 mph when expressed in miles per hour. Among the given options, that rough magnitude is the best match to the statement, since the other numbers are either far too small or clearly not in the same rough range. For context, the more precise measurement of the Sun’s actual orbital speed is about 220 km/s, which is roughly 490,000 mph, illustrating that the true value sits in the 10^5–10^6 mph range. The question uses a simplified figure, so selecting the option describing about 100,000 mph aligns with that approachable estimate.

In an LC circuit the capacitor and inductor exchange energy back and forth, so the system tends to ring at its own natural rate. The math shows the charge on the capacitor (and the current in the loop) varies with angular frequency ω0 = 1/√(LC), giving a regular frequency f0 = 1/(2π√(LC)). This intrinsic frequency is what the circuit would oscillate at if it weren’t driven by an external source and unless some resistance damps it. That makes it the natural, or resonant, frequency. It’s not the external (applied) frequency, and terms like cutoff relate to filters rather than the free oscillation, while imaginary frequency isn’t a physical description of this real oscillator.

ε0 is the permittivity of free space, the constant that sets how electric fields behave in vacuum. It tells you how much electric field is produced by a given charge in empty space and appears directly in Coulomb’s law through the factor 1/(4π ε0), which governs the strength of electrostatic forces between charges. In vacuum, the electric displacement D relates to the electric field E by D = ε0 E, so ε0 links the field to how the space responds to it. This constant also connects electric and magnetic phenomena: the speed of light c satisfies c^2 = 1/(μ0 ε0), tying ε0 to μ0, the permeability of free space, and showing how electromagnetic waves propagate in vacuum. The value is about 8.854 × 10^-12 farads per meter (F/m). The other options describe different concepts: permeability of free space is μ0, not ε0; electrical conductivity of air is a material property that varies with conditions; and electrical resistance of vacuum isn’t a standard constant (the relevant vacuum property is the impedance of free space, Z0, not a resistance).