A 60W light bulb is connected to a 120V outlet. How long in seconds does it take for 1 billion (109) electrons to pass through the light bulb?
The current will be
I = P/V = 60/120 = 0.5 A
which is 0.5 Coulombs per second.
10^9 electrons will pass through in time t such that
(0.5 C/s)* t = 10^9(electrons)*1.6*10^-19 (C/electron)
t = 3.2*10^-10 s
To determine the time it takes for 1 billion electrons to pass through the light bulb, we need to calculate the number of electrons passing through the bulb per second.
Let's start by calculating the charge of a single electron.
The charge of an electron is approximately 1.602 x 10^-19 coulombs.
Since we know that the power of the light bulb is 60W, we can use the formula:
Power (in watts) = Current (in amperes) x Voltage (in volts)
Rearranging the formula to solve for the current:
Current = Power / Voltage
Substituting the values:
Current = 60W / 120V
Current = 0.5 A
Now, we can calculate the number of electrons passing through the light bulb per second.
Number of electrons = Current / Charge of a single electron
Number of electrons = 0.5 A / 1.602 x 10^-19 C
Number of electrons ≈ 3.12 x 10^18 electrons per second
Finally, we can calculate the time it takes for 1 billion electrons (1 x 10^9) to pass through the light bulb.
Time = Number of electrons to pass / Number of electrons per second
Time = (1 x 10^9) electrons / (3.12 x 10^18) electrons per second
Time ≈ 0.32 seconds
Therefore, it takes approximately 0.32 seconds for 1 billion electrons to pass through the light bulb.