Inductive reactance (X_L) is given by X_L = 2πfL. If the frequency (f) is doubled, X_L also doubles.

The reactance of an inductor is given by X_L = 2πfL. If frequency is doubled, reactance halves.

The power factor is cos(θ). If PF = 0.5, then θ = cos^(-1)(0.5) = 60 degrees.

A power factor of 1 indicates a purely resistive load.

For a resistor, the current is in phase with the voltage. Therefore, I(t) = V(t)/R = (V_0/R) sin(ωt).

Using the formula for the nth term: a_n = a + (n-1)d, we have 45 = 5 + 9d. Solving gives d = 4.

Power in an electric circuit is given by P = V * I. Here, P = 12 V * 3 A = 36 W.

Power in an electric circuit is given by P = V^2/R. If V is doubled, P becomes (2V)^2/R = 4V^2/R, which is quadrupled.

In an endothermic reaction, the enthalpy of the products is higher than that of the reactants.

Range = Measured value ± Uncertainty = 200 g ± 5 g = 195 g to 205 g.

Total uncertainty = 3 * (0.5 m) = ±1.5 m.

Absolute error is the uncertainty in the measurement, which is ±0.2 kg.

Maximum possible error is equal to the uncertainty, which is ±0.2 V.

The absolute error is given as ±0.3 V.

The absolute error is given directly as ±0.5 V.

The maximum possible error is the absolute uncertainty, which is ±0.5 V.

The average kinetic energy of a molecule in an ideal gas is directly proportional to the absolute temperature (T) of the gas.

The average kinetic energy of a molecule in an ideal gas is directly proportional to the absolute temperature of the gas, given by the formula KE_avg = (3/2)kT.

The mean free path is affected by temperature, density, and size of the molecules, but not by the color of the gas molecules.

According to Gay-Lussac's law, for a fixed amount of gas at constant volume, the pressure is directly proportional to the absolute temperature.

The root mean square speed of gas molecules is given by the formula v_rms = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass.

In an ideal gas, the volume occupied by the gas molecules is considered negligible compared to the total volume of the gas.

In an isothermal process, the temperature of the gas remains constant.

In an ideal solution, the enthalpy of mixing is zero, indicating no heat is absorbed or released during mixing.

In an irreversible process, the change in entropy of the universe is positive, indicating that the total entropy increases.

An isochoric process is characterized by constant volume, meaning the volume does not change.

In an isochoric process, the volume remains constant, and any heat added to the system increases the internal energy.

In an isochoric process, the volume remains constant, and any heat added increases the internal energy of the gas.

In an isothermal process, the temperature remains constant, which implies that the internal energy of an ideal gas also remains constant.

In an isothermal process for an ideal gas, the temperature remains constant, and thus the internal energy also remains constant.