A 1.50-V battery supplies 0.244 W of power to a small flashlight. If the battery moves 2.53 1020 electrons between its terminals during the time the flashlight is in operation, how long was the flashlight used?
numberelectrons*charge/electron*Voltage*timeinSeconds=.244
solve for time
To find the time the flashlight was used, we can use the formula:
Power (P) = Voltage (V) × Current (I)
We are given the voltage (V) of the battery as 1.50 V, and the power (P) consumed by the flashlight as 0.244 W.
Let's first find the current (I):
P = V × I
0.244 W = 1.50 V × I
Now, divide both sides of the equation by 1.50 V to solve for I:
I = 0.244 W / 1.50 V
Next, we need to find the amount of charge (Q) passing through the battery terminals. We are given that the battery moves 2.53 × 10^20 electrons. To convert this to the amount of charge, we can use the elementary charge (e) as follows:
Q = (2.53 × 10^20 electrons) × (1.60 × 10^-19 C/electron)
Now, we can calculate the time (t) using the formula:
Q = I × t
t = Q / I
Substitute the values:
t = [(2.53 × 10^20 electrons) × (1.60 × 10^-19 C/electron)] / (0.244 W / 1.50 V)
Calculating the expression in the numerator:
t = (4.048 × 10) / (0.1629)
t ≈ 2490.44 seconds
Therefore, the flashlight was used for approximately 2490.44 seconds.
To find the time the flashlight was used, we can use the equation relating power, voltage, and current. The equation is:
Power (P) = Voltage (V) * Current (I)
Here, we are given the power (P = 0.244 W) and the voltage (V = 1.50 V). We need to find the current (I) to calculate the time.
To find the current, we can use the equation relating current, quantity of charge (Q), and time (t):
Current (I) = Quantity of Charge (Q) / Time (t)
In the question, we are given that 2.53 * 10^20 electrons move during the operation of the flashlight. We know that one electron has a charge of 1.6 * 10^-19 Coulombs. So we can calculate the quantity of charge (Q) as follows:
Quantity of Charge (Q) = Number of Electrons * Charge of One Electron
Now we can plug in the values we have:
Quantity of Charge (Q) = (2.53 * 10^20) * (1.6 * 10^-19)
Once we have the quantity of charge, we can rearrange the equation to solve for time:
Time (t) = Quantity of Charge (Q) / Current (I)
To calculate the current (I), we can rearrange the equation relating power, voltage, and current:
Current (I) = Power (P) / Voltage (V)
Now we can substitute the values we have:
Current (I) = 0.244 W / 1.50 V
Finally, we can substitute the calculated current (I) and quantity of charge (Q) into the equation to find the time (t):
Time (t) = (2.53 * 10^20) * (1.6 * 10^-19) / (0.244 W / 1.50 V)
Calculating this expression will give us the time the flashlight was used.