Alkaline batteries have the advantage of putting out constant voltage until very nearly the end of their life. How long will an alkaline battery rated at 1 A ⋅ h and 1.58 V keep a 1 W flashlight bulb burning?
P = E*I = 1.0 W.
1.58I = 1.0
I = 0.633A.
A*h = 1.
0.633*h = 1.
h = 1.58 Hours.
MITA VITTUA
To calculate the amount of time an alkaline battery will keep a 1 W flashlight bulb burning, we can use the formula:
t = (Q * V) / P
where:
t = time (in hours)
Q = battery capacity (in amp-hours)
V = battery voltage (in volts)
P = power (in watts)
In this case, the battery capacity is 1 A ⋅ h, the battery voltage is 1.58 V, and the power is 1 W.
Plugging these values into the formula, we have:
t = (1 A ⋅ h * 1.58 V) / 1 W
t = (1.58 V ⋅ A ⋅ h) / 1 W
Next, we need to convert the units to match. Since we know that 1 W = 1 J/s, we can convert from amp-hours to watt-hours:
1 A ⋅ h = 1 A ⋅ h * (1 W / 1 J/s) * (3600 s / 1 h)
1 A ⋅ h = 3600 J
Now, we can substitute the values into the formula again:
t = (1.58 V ⋅ 3600 J) / 1 W
Simplifying:
t = 5704.8 J / 1 W
t = 5704.8 s
Therefore, an alkaline battery rated at 1 A ⋅ h and 1.58 V will keep a 1 W flashlight bulb burning for approximately 5704.8 seconds, or approximately 1.58 hours.
To determine how long an alkaline battery will keep a 1 W flashlight bulb burning, we need to calculate the battery life in hours.
Given information:
- Battery capacity: 1 A⋅h
- Battery voltage: 1.58 V
- Power consumption of the bulb: 1 W
First, we need to calculate the current consumed by the bulb using Ohm's Law (P = IV), where P represents power and I represents current.
Rearranging the formula gives us I = P / V, where I is the current.
Using the given power and voltage values:
I = 1 W / 1.58 V
I ≈ 0.633 A (rounded to 3 decimal places)
Now, to find the battery life, we divide the battery capacity by the current:
Battery life = Battery capacity / Current
Battery life = 1 A⋅h / 0.633 A
Battery life ≈ 1.58 hours (rounded to 2 decimal places)
Therefore, an alkaline battery with a capacity of 1 A⋅h and a voltage of 1.58 V will keep a 1 W flashlight bulb burning for approximately 1.58 hours.