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.

Moles = Molarity * Volume = 3 mol/L * 2 L = 6 moles.

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 Tyndall effect is the scattering of light by colloidal particles, making the path of the light visible.

The unit of electric charge is Coulomb (C).

The unit of electrical conductivity is Siemens (S).

The unit of the rate constant for a first-order reaction is s⁻¹.

The SI unit of work is Joule (J).

Magnesium has a valency of 2, as it can lose two electrons.

Oxygen has a valency of 2, as it needs two electrons to complete its outer shell.

(1 + i)(1 - i) = 1^2 - i^2 = 1 - (-1) = 1 + 1 = 2.

Using BODMAS: (2 + 3) = 5 and (4 - 1) = 3, so 5 × 3 = 15.

(2 + 3) × 4 = 5 × 4 = 20.

Using the binomial theorem, (2 + 3)^3 = C(3,0)(2)^3 + C(3,1)(2)^2(3) + C(3,2)(2)(3)^2 + C(3,3)(3)^3 = 8 + 36 + 54 + 27 = 125.

Multiply numerator and denominator by the conjugate of the denominator: (2 + 3i)(1 - i) / (1 + i)(1 - i) = (2 - 2i + 3i + 3) / (1 + 1) = (5 + i) / 2 = 2.5 + 0.5i.

Using the difference of squares: (a + b)(a - b) = a² - b². Here, (2)² - (3i)² = 4 - (-9) = 4 + 9 = 13.

Using the binomial theorem, (2 - 3)^5 = (-1)^5 = -1.

Multiplying numerator and denominator by the conjugate of the denominator: (3 + 4i)(1 - i) / (1 + i)(1 - i) = (3 - 3i + 4i + 4) / 2 = (7 + i) / 2 = 2 + i.

(3 + 5) = 8 and (2 + 4) = 6, so 8 × 6 = 48.