The total resistance in series is R_total = R1 + R2 = 4Ω + 6Ω = 10Ω.

Using the formula for resistors in series, R_total = R1 + R2, we have 12 = 4 + R2, thus R2 = 12 - 4 = 8 ohms.

Using the voltage divider rule, V1 = (R1 / (R1 + R2)) * Vtotal = (4 / (4 + 6)) * 12 = 4.8V.

Using the voltage divider rule, V1 = (R1 / (R1 + R2)) * Vtotal = (4 / (4 + 6)) * 12 = 4.8V.

Using Ohm's law, R = V/I = 12V / 3A = 4 ohms.

According to Ohm's law, if voltage is doubled and resistance remains constant, current also doubles.

According to Ohm's law, if voltage is halved while resistance remains constant, current also halves.

Initial current I1 = 5V / 5Ω = 1 A; Final current I2 = 15V / 5Ω = 3 A; Change in current = I2 - I1 = 3 A - 1 A = 2 A.

According to Ohm's Law, if voltage increases and resistance remains constant, the current will increase.

According to Ohm's Law, if the voltage (V) increases and resistance (R) remains constant, the current (I) increases.

According to Kirchhoff's current law, the current flowing into the junction must equal the current flowing out. Therefore, 10A - 6A = 4A is the current flowing through the junction.

According to Kirchhoff's Voltage Law, the net voltage in the loop is the sum of rises minus the sum of drops: 10V - 6V = 4V.

According to Kirchhoff's Voltage Law, the net voltage in the loop is the sum of voltage rises minus the sum of voltage drops: 20V - 15V = 5V.

Resistance R = ρ(L/A) = 2 x 10^-8 * (10 / (1 x 10^-6)) = 0.2 Ω.

Resistance R = ρ(L/A) = 2 x 10^-8 * (3 / (1 x 10^-6)) = 0.024 Ω.

The equivalent resistance for resistors in parallel is given by 1/R_eq = 1/R1 + 1/R2 + 1/R3. Thus, 1/R_eq = 1/2 + 1/3 + 1/6 = 1. Therefore, R_eq = 1Ω.

Using the formula for resistors in parallel, 1/R_eq = 1/R1 + 1/R2 + 1/R3, we find R_eq = 1 / (1/6 + 1/12 + 1/18) = 3 ohms.

1/R_eq = 1/R1 + 1/R2 + 1/R3 = 1/2 + 1/3 + 1/6 = 1. Therefore, R_eq = 3Ω.

The formula for equivalent resistance in parallel is 1/R_eq = 1/R1 + 1/R2 + 1/R3. Thus, 1/R_eq = 1/6 + 1/3 + 1/2 = 1/6 + 2/6 + 3/6 = 6/6 = 1, so R_eq = 1 ohm.

The equivalent resistance in parallel is given by 1/R_total = 1/R1 + 1/R2 + 1/R3. Thus, 1/R_total = 1/2 + 1/3 + 1/6 = 1Ω.

For parallel resistors, 1/R_eq = 1/R1 + 1/R2. Thus, 1/R_eq = 1/4 + 1/6 = 5/12, so R_eq = 12/5 = 2.4 ohms.

First, find the equivalent resistance: 1/R_eq = 1/4 + 1/6 => R_eq = 2.4 ohms. Then, I = V/R_eq = 12V / 2.4Ω = 5 A.

First, find the equivalent resistance: 1/R_eq = 1/4 + 1/6 => R_eq = 2.4 ohms. Then, I = V/R_eq = 12 V / 2.4 ohms = 5 A.

First, find the equivalent resistance: 1/R_eq = 1/4 + 1/6 => R_eq = 2.4Ω. Then, I = V/R_eq = 12V / 2.4Ω = 5A.

Using the formula for resistors in parallel, 1/R_eq = 1/R1 + 1/R2, we have 1/R_eq = 1/6 + 1/3 = 1/6 + 2/6 = 3/6. Therefore, R_eq = 6/3 = 2 ohms.

1/R_eq = 1/R1 + 1/R2 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, thus R_eq = 2Ω.

In a parallel circuit, if one resistor fails, the total current decreases because the total resistance increases.

In a parallel circuit, removing a resistor decreases the total resistance.

The potential gradient is V/L = 1.5V/0.5m = 3 V/m, but since the total length is 1m, the gradient is 1.5 V/m.

The potential gradient is defined as the potential difference per unit length. If the length is doubled while keeping the potential difference constant, the potential gradient halves.