Using Ohm's law, V = I * R = 2A * 12Ω = 24 V.

Power P = V^2 / R = (24V)^2 / 12Ω = 48 W.

Using Ohm's law, I = V/R = 48V / 12Ω = 4 A.

Power P = V²/R = 24² / 12 = 48 W.

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

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

Using Ohm's Law, I = V/R = 12 V / 4 Ω = 3 A.

The capacitance increases by a factor equal to the dielectric constant. Thus, it quadruples.

The capacitance increases by the factor of the dielectric constant, so C' = k * C, where k = 4.

The time constant τ = R * C = 10 ohms * 100 x 10^-6 F = 0.001 seconds or 1 millisecond.

Using Ohm's Law, I = V/R. Here, I = 5V / 10Ω = 0.5 A.

R_total = R1 + R2 = 10 Ω + 20 Ω = 30 Ω.

Total resistance in series is R_total = R1 + R2 = 10 Ω + 5 Ω = 15 Ω.

Power P = V²/R = (20V)² / 10Ω = 400/10 = 40 W.

Doubling the capacitance in an RC circuit will double the time constant τ = R * C.

Charge (Q) is given by Q = C * V. Here, Q = 3 µF * 6 V = 18 µC.

Charge (Q) stored in a capacitor is given by Q = C * V. If C is doubled and V remains constant, Q also doubles.

Capacitance (C) is defined as C = Q/V. If C is doubled and V remains constant, Q must also double.

According to Coulomb's law, the force F between two point charges is inversely proportional to the square of the distance r between them. If the distance is doubled, the force becomes F/4.

Potential difference V = E * d = 2000 N/C * 0.05 m = 100 V.

Potential energy U = V * q = 100 V * 2 x 10^-6 C = 0.0002 J = 0.2 J.

Q = C * V = 3 x 10^-6 F * 12 V = 36 µC.

Energy stored in a capacitor is given by U = 1/2 C V^2. If V is doubled, U becomes 1/2 C (2V)^2 = 2CV^2, which is quadrupled.

According to Ohm's Law, if voltage is doubled and resistance is constant, current will also double.

For capacitors in series, the total capacitance is given by 1/C_total = 1/C1 + 1/C2.

C_eq = C1 + C2 = 4 µF + 6 µF = 10 µF.

1/C_total = 1/C1 + 1/C2 = 1/4 + 1/6 = 5/12, thus C_total = 12/5 = 2.4 µF.

The equivalent capacitance for capacitors in series is given by Ceq = 1 / (1/C1 + 1/C2).

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |3 x 10^-6 C * -3 x 10^-6 C| / (0.2 m)^2 = 45 N.

At the midpoint, the electric fields due to both charges cancel each other out, resulting in E = 0.