Final answer:
To find the power dissipated in a cable per unit length, use the formula P = I²R, where P is the power, I is the current, and R is the resistance. For an extension cord with a resistance of 0.0600 ohms and a current of 5.00 A, 1.50 W is dissipated; for one with 0.300 ohms, it's 7.50 W. Divide the power by the cable length to get the power per unit length.
Step-by-step explanation:
To determine the power dissipated in a cable per unit length, one can use the formula P = I²R, where P is the power in watts, I is the current in amperes, and R is the resistance in ohms. For example, for an extension cord with a resistance of 0.0600 ohms and a current of 5.00 A flowing through it, the power dissipated can be calculated as follows:
P = I²R = (5.00 A)² × 0.0600 Ω = 1.50 W
This is the power dissipated over the entire length of the extension cord. If you must find the power dissipated per unit length, you would divide this power by the length of the extension cord. Similarly, if another cord has a resistance of 0.300 ohms, the power dissipated by that cord would be:
P = I²R = (5.00 A)² × 0.300 Ω = 7.50 W
Again, dividing by the length of the cable would give the power dissipated per unit length. These calculations are essential for ensuring electrical safety and efficiency in circuit design and power management.