As the capacitor charges, the current decreases exponentially until it approaches zero.

The time constant τ in a series RC circuit is defined as τ = R * C, where R is resistance and C is capacitance.

The peak voltage is the coefficient of the sine function, which is 10 V.

Total resistance R_total = R1 + R2 = 4Ω + 8Ω = 12Ω. Using Ohm's Law, I = V / R_total = 12V / 12Ω = 1A.

In the transient response of an RC circuit, the current decreases exponentially as the capacitor charges.

In an AC circuit, the voltage is related to current and impedance by V = I * Z.

In a purely resistive AC circuit, the voltage and current are in phase, meaning they reach their maximum and minimum values at the same time.

The maximum voltage in an AC circuit is referred to as the peak voltage.

When the capacitor is fully charged, the current through the circuit is zero because the capacitor blocks any further current flow.

As time approaches infinity, the capacitor becomes fully charged and the current approaches the maximum value V/R, where V is the voltage and R is the resistance.

As time approaches infinity, the capacitor charges to the supply voltage, so the voltage across it equals the supply voltage.

The cutoff frequency f_c is related to the time constant by the formula f_c = 1 / (2πτ).

The time constant τ in an RC circuit is defined as τ = R*C, where R is the resistance and C is the capacitance.

Time constant τ = R * C = (2000 Ω) * (10 x 10^-6 F) = 0.02 s = 20 ms.

Time constant τ = R * C = 4000 Ω * 10 x 10^-6 F = 40 ms.

The electric fields due to both charges at the midpoint are equal in magnitude and opposite in direction, resulting in a net electric field of 0 N/C.

Total resistance R = 3Ω + 4Ω = 7Ω. Total current I = V/R = 12V / 7Ω = 1.71A. Voltage drop across 3Ω = I * R = 1.71A * 3Ω = 5.14V.

Using KVL, V_total = V_R1 + V_R2. V_R1 = 20V - (I * 5Ω). I = V/R = 20V / 15Ω = 1.33 A. V_R1 = 10Ω * 1.33 A = 13.33V.

Capacitance is directly proportional to the plate area. Doubling the area doubles the capacitance.

The charge on a discharging capacitor decreases exponentially over time.

As time approaches infinity after the switch is closed, the current in an RC circuit decreases to zero.

As a positive charge moves away from another positive charge, the electric potential energy decreases due to the repulsive force.

When capacitors are connected in series, the total capacitance decreases and is given by the formula 1/C_total = 1/C1 + 1/C2 + ... + 1/Cn.

The capacitance of a parallel plate capacitor is given by C = ε * A / d, where ε is the permittivity of the dielectric.

C = Q / V = 0.01 C / 5 V = 0.002 F.

Using the formula C = Q/V = 0.01 C / 5 V = 0.002 F.

Using U = 1/2 C V^2, rearranging gives C = 2U/V^2 = 2(0.01 J)/(10 V)^2 = 0.1 F.

Capacitance C = Q/V = 0.02 C / 10 V = 0.002 F = 0.2 F.

C = Q/V = 20 x 10^-6 C / 5 V = 4 µF.

C = Q/V = 12 x 10^-6 C / 6 V = 2 x 10^-6 F = 2 µF.