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 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 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.

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

Work = F × d × cos(θ) = 15 N × 4 m × cos(60°) = 15 × 4 × 0.5 = 30 J.

Work done (W) = P * ΔV = 3 atm * (5 L - 2 L) = 3 atm * 3 L = 9 atm·L = 15 J (1 atm·L = 101.325 J)

Work done (W) = P * ΔV = 2 atm * (2 L - 4 L) = 2 atm * (-2 L) = -4 L·atm (work done on the gas is positive).

Work done (W) = P * ΔV = 200 kPa * (2 L - 5 L) = 200 kPa * (-3 L) = -600 J (work done on the gas).

Work done (W) = nRT ln(Vf/Vi) = 1 mol * 8.314 J/(mol K) * 300 K * ln(20/10) = 2.5 kJ.

Work done W = nRT ln(Vf/Vi) = 1 * 8.314 * 300 * ln(20/10) = 600 J.

Work done = nRT ln(Vf/Vi) = 1 mol × 8.31 J/mol·K × 300 K × ln(20/10) = 1660 J.

Work done (W) = F × d = 50 N × 3 m = 150 J.