Question 17.1: Turn on the Light Goal Apply the concept of current. Problem...
Turn on the Light
Goal Apply the concept of current.
Problem The amount of charge that passes through the filament of a certain lightbulb in 2.00 s is 1.67 C. Find (a) the current in the bulb and (b) the number of electrons that pass through the filament in 5.00 s.
Strategy Substitute into Equation 17.1 for part (a), then multiply the answer by the time given in part (b) to get the total charge that passes in that time. The total charge equals the number N of electrons going through the circuit times the charge per electron.
I \equiv \frac{\Delta Q}{\Delta t}
(a) Compute the current in the lightbulb.
Substitute the charge and time into Equation 17.1:
I=\frac{\Delta Q}{\Delta t}=\frac{1.67 C }{2.00 s }=0.835 A
(b) Find the number of electrons passing through the filament in 5.00 s.
The total number N of electrons times the charge per electron equals the total charge, I Δt:
N q=I \Delta t (1)
Substitute and solve for N:
\begin{aligned}&N\left(1.60 \times 10^{-19} \text { C/electron }\right)=(0.835 A )(5.00 s ) \\&N=2.61 \times 10^{19} \text { electrons }\end{aligned}
Remarks In developing the solution, it was important to use units to ensure the correctness of equations such as Equation (1). Notice the enormous number of electrons passing through a given point in a typical circuit.