Final answer:
The hot resistance of a 30.0-W headlight in a car with a 6.00-V electrical system is 1.20 ohms and the current flowing through it is 5.00 A.
Step-by-step explanation:
To determine the hot resistance of a 30.0-W headlight in a car with a 6.00-V electrical system, we use the formula P = V^2/R, where P is power, V is voltage, and R is resistance. Rearranging the formula to solve for R gives us R = V^2/P.
Using the headlight's power (P = 30.0 W) and the car's voltage (V = 6.00 V), we find:
- R = (6.00^2) / 30.0 = 36 / 30.0 = 1.20 ohms.
The current (I) through the headlight is found using Ohm's law, I = P/V.
- I = 30.0 W / 6.00 V = 5.00 A.
Therefore, the headlight has a hot resistance of 1.20 ohms, and the current that flows through it is 5.00 A.