To determine the number of electrons that pass through a headlight each second, we need to calculate the current flowing through it and then use the concept of charge.
First, let's find the current (I) flowing through the headlight using Ohm's Law:
I = P / V
Where: I is the current (in Amperes, A) P is the power (in Watts, W) V is the voltage (in Volts, V)
In this case, the power (P) of the headlight is 30.0 W, and the voltage (V) of the car battery is 12.0 V.
I = 30.0 W / 12.0 V I ≈ 2.5 A
Now that we have the current, we can calculate the number of electrons passing through the headlight each second using the equation:
Q = I * t
Where: Q is the charge (in Coulombs, C) I is the current (in Amperes, A) t is the time (in seconds, s)
The charge (Q) represents the total number of electrons passing through the headlight since each electron carries a charge of 1.6 x 10^(-19) C.
Q = (2.5 A) * (1 s) Q = 2.5 C
Now, we can find the number of electrons (N) by dividing the total charge by the charge carried by a single electron:
N = Q / e
Where: N is the number of electrons Q is the charge (in Coulombs, C) e is the charge of a single electron (approximately 1.6 x 10^(-19) C)
N = 2.5 C / (1.6 x 10^(-19) C) N ≈ 1.5625 x 10^19
Therefore, approximately 1.5625 x 10^19 electrons pass through the headlight each second when a 12.0V car battery powers a single 30.0W headlight.