The energy stored in a capacitor is given by U = 1/2 CV^2. If V is halved, the energy becomes U' = 1/2 C(V/2)^2 = 1/8 CV^2, which is halved.

The charge (Q) stored in a capacitor is directly proportional to the potential difference (V) across it, given by Q = CV.

Work done (W) = Charge (Q) × Potential difference (V) = 2 C × 10 V = 20 J.

Linear velocity v = rω, so if r is halved and ω remains constant, v also halves.

The focal length (f) of a concave mirror is given by f = R/2, where R is the radius of curvature. Thus, f = 20 cm / 2 = 10 cm.

The focal length f of a lens is given by f = R/2. Therefore, f = 20 cm / 2 = 10 cm.

The focal length (f) of a mirror is given by f = R/2. For a convex mirror, R is positive, so f = 20 cm / 2 = 10 cm.

According to Ohm's Law, if the resistance (R) is doubled and the voltage (V) remains constant, the current (I) will be halved (I = V/R).

Relative lowering of vapor pressure = (P° - P) / P° = (100 - 80) / 100 = 0.2.

Using Raoult's Law: P_solution = X_solvent * P_solvent. X_solvent = P_solution / P_solvent = 80/100 = 0.8, thus X_solute = 1 - X_solvent = 0.2.

The peak voltage (V_peak) is calculated as V_peak = V_rms × √2 = 100 V × √2 ≈ 141.42 V.

According to Ohm's law, if voltage increases and resistance remains constant, current will also increase proportionally.

Inductive reactance (X_L) is given by X_L = V/I. Here, X_L = 100 V / 2 A = 50 Ω.

The electric fields due to both charges at the midpoint cancel each other out, resulting in a net electric field of 0 N/C.

Total resistance R = 4Ω + 12Ω = 16Ω. Voltage V = I * R = 2A * 16Ω = 32V.

Using the formula for parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6 = 5/12, R_eq = 12/5 = 2.4Ω.

In series, R_total = R1 + R2 = 5Ω + 10Ω = 15Ω.

In a body-centered cubic (BCC) structure, there are 2 atoms per unit cell (1 from the center and 1 from the corners).

Increasing the plate area while keeping the distance constant increases the capacitance, as capacitance is directly proportional to the area of the plates.

Activation energy is the minimum energy required to initiate a chemical reaction.

Power P = V^2/R = 5^2/10 = 25/10 = 2.5W.

Total resistance R = 10Ω + 5Ω = 15Ω. Voltage V = I * R = 2A * 15Ω = 30V.

Total resistance R = 4Ω + 4Ω = 8Ω. Current I = V/R = 12V/8Ω = 1.5A.

The voltage drop across the resistor is equal to the battery voltage, which is 15V.

The total resistance is 15Ω. The current I = V/R = 15V/15Ω = 1A. Voltage drop across 10Ω = I * R = 1A * 10Ω = 10V.

Power (P) can be calculated using P = V^2 / R. Here, P = 24V^2 / 6Ω = 96W.

Power P = V^2/R = 24^2/8 = 576/8 = 72 W.

Total resistance R_total = 3Ω + 6Ω = 9Ω. Current I = V/R_total = 9V/9Ω = 1A. Voltage across 6Ω = I * R = 1A * 6Ω = 6V.

Total resistance R = 3Ω + 6Ω = 9Ω. Current I = V/R = 9V/9Ω = 1A.

Using Ohm's Law, R = V/I = 24V / 6A = 4Ω.