When two resistors are connected in series, their resistances add up. Thus, the combined resistance of two 1 kilo ohm resistors connected in series can be calculated as follows:

Combined Resistance = R1 + R2

where R1 and R2 are the individual resistances of the two resistors.

In this case, R1 = R2 = 1 kilo ohm. Therefore,

Combined Resistance = 1 kilo ohm + 1 kilo ohm = 2 kilo ohms



When two resistors are connected in series, the current passing through both resistors is the same. However, the voltage across each resistor may be different, depending on their individual resistances. The power dissipated by each resistor can be calculated using the formula:

Power = (Voltage)^2 / Resistance

The total power dissipated by both resistors can be calculated by adding up their individual powers. Thus, the combined wattage of two 1/2 W resistors connected in series can be calculated as follows:

Power1 = (Voltage1)^2 / R1
Power2 = (Voltage2)^2 / R2

Since the voltage across both resistors is the same, we can simplify the equation to:

Power1 = Power2 = (Voltage)^2 / R

where R is the combined resistance of the two resistors.

Substituting the values, we get:

Power1 = Power2 = (Voltage)^2 / 2 kilo ohms

Since the total power dissipated is the sum of Power1 and Power2, we can write:

Total Power = Power1 + Power2 = 2 * (Voltage)^2 / 2 kilo ohms

Simplifying the equation, we get:

Total Power = (Voltage)^2 / kilo ohms

Since the total power is 1 W (the sum of the powers of the two 1/2 W resistors), we can write:

1 W = (Voltage)^2 / 2 kilo ohms

Solving for Voltage, we get:

Voltage = sqrt(2 kilo ohms * 1 W) = sqrt(2000) V

Voltage = 44.72 V (rounded to two decimal places)

Substituting the values in the equation for Power, we get:

Total Power = (44.72 V)^2 / 2 kilo ohms = 1 W

Therefore, the combined resistance of two 1 kilo ohm, 1/2 W resistors connected in series is 2 kilo ohms and their combined wattage is 1 W.