The speed of light in vacuum is approximately 3 x 10^8 m/s.

To convert Kelvin to Celsius, use the formula: °C = K - 273. Therefore, 273 K - 273 = 0°C.

Temperature in Kelvin (K) = Temperature in Celsius (°C) + 273.15 = 25 + 273.15 = 298.15 K.

Using the formula Q = kA(T1-T2)t, we find k = Q / (A(T1-T2)t) = 100 J / (1 m² * 20°C * 10 s) = 0.5 W/m°C.

The time period T is the reciprocal of frequency, T = 1/f. Thus, T = 1/20 Hz = 0.05 s.

Using Ohm's law, I = V/R = 9V / 3Ω = 3A.

Total resistance R = 5Ω + 5Ω = 10Ω; I = V/R = 15V / 10Ω = 1.5A.

Z = √(R² + Xl²) = √(20² + 30²) = √(400 + 900) = √1300 = 36.06 ohms. I = V/Z = 240/36.06 = 6.66 A.

In parallel circuits, the total current is the sum of the currents in each branch: I_total = 3A + 2A = 5A.

In a parallel circuit, the total current (I_total) is the sum of the currents in each branch: I_total = 3A + 5A = 8A.

Total current in parallel = I1 + I2 = 5A + 3A = 8A.

Total impedance Z = √(R² + (ωL)²) = √(10² + (2π(50)(20))²). Calculate to find current.

At the highest point of a pendulum's swing, all the mechanical energy is potential energy, and kinetic energy is zero.

At maximum displacement, the total mechanical energy of a simple harmonic oscillator is at its maximum, as all energy is potential.

The total mechanical energy E is given by E = (1/2)kA². Therefore, E = (1/2)(100)(0.1)² = 0.5 J.

At the highest point of a projectile's trajectory, the kinetic energy is minimum (zero at the peak) and potential energy is maximum, thus total mechanical energy is maximum potential energy.

Total resistance R = 10Ω + 10Ω = 20Ω. Power P = V²/R = 20² / 20 = 20W.

Total resistance R = 5Ω + 5Ω = 10Ω; Power P = V²/R = 30²/10 = 90W.

In series, R_eq = R1 + R2 = 10Ω + 20Ω = 30Ω.

In series, R_eq = R1 + R2 = 10Ω + 20Ω = 30Ω.

In series, R_total = R1 + R2 = 4Ω + 6Ω = 10Ω.

In a series circuit, total resistance (R_total) is the sum of individual resistances: R_total = R1 + R2 + R3 = 2Ω + 3Ω + 5Ω = 10Ω.

In series, R_eq = R1 + R2 = 4Ω + 4Ω = 8Ω.

For parallel resistors, 1/R_eq = 1/R1 + 1/R2 = 1/4 + 1/6. Finding a common denominator gives R_eq = 2.4Ω.

The unit of electric charge is Coulomb (C).

The SI unit of work is Joule (J).

Using Ohm's law, V = IR = 3A * 10Ω = 30V.

Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.

Using Ohm's law, V = IR = 3A * 12Ω = 36V.

Using Ohm's law, V = IR = 3A * 5Ω = 15V.