A resistor in series with a 100-R resistor absorbs 80 W when the two are connected across a 240-V line.Find the unknown resistance

Sure, let's solve this step by step.

Step 1: Understand the problem We have a 100-ohm resistor in series with an unknown resistor. The total power absorbed by the circuit is 80W when connected to a 240V line. We need to find the resistance of the unknown resistor.

Step 2: Use Ohm's Law Ohm's law states that V = IR, where V is voltage, I is current, and R is resistance.

Step 3: Use the power formula The power formula is P = IV, where P is power, I is current, and V is voltage.

Step 4: Calculate the total current in the circuit We know the total power (P) is 80W and the voltage (V) is 240V. We can rearrange the power formula to find the current: I = P/V = 80W / 240V = 0.333A.

Step 5: Calculate the total resistance in the circuit Using Ohm's law, we can find the total resistance: R = V/I = 240V / 0.333A = 720 ohms.

Step 6: Calculate the unknown resistance We know the total resistance (720 ohms) and the resistance of the known resistor (100 ohms). The resistors are in series, so the total resistance is the sum of the individual resistances. Therefore, the unknown resistance is 720 ohms - 100 ohms = 620 ohms.

So, the unknown resistance is 620 ohms.