How Much Energy Does a Linearly Declining Battery Voltage Deliver Over Time?

  • Thread starter Thread starter math1280
  • Start date Start date
  • Tags Tags
    Battery Energy
AI Thread Summary
The discussion focuses on calculating the energy delivered by a battery with a linear voltage decline from 1.5V to 1.0V over 40 hours while providing a constant current of 9mA. The user derived a power function and integrated it to find the energy delivered, resulting in 1622.6J. However, a discrepancy arose when comparing this calculation to the area under a graph of power versus time, which yielded only 324J. The issue was identified as an error in calculating the area under the graph, specifically only considering the triangular area rather than the entire shape. Accurate calculations and graph assessments are crucial for resolving such discrepancies.
math1280
Messages
2
Reaction score
0

Homework Statement


A battery provides a continuous current of 9mA (.009A) for 40hrs (144,000sec). During that time the voltage drops from 1.5 to 1.0. Assume the drop is linear with time. How much energy does the battery deliver during this 40hr interval



Homework Equations


P=IV


The Attempt at a Solution


First I found an equation for voltage as a function of time (s) V(t)=1.5-3.472x10^-6t.
Then I figured power as a function of time P(t)=IxV(t)=.009(1.5-3.472x10^-6t)
P(t)=.0135-3.1x10^-8t. To find the energy delivered, I integrated P(t) so that E=.0135t-3.1x10^8t^2/2. The limits were from 0 to 144,000. I ended up with 1944-321.408=1622.6J
My problem is that when I just made a graph of power vs time and found the area under it from 0 to 144,000 I got 324J. Could I please get some guidance as to what I'm doing wrong?
 
Physics news on Phys.org
Check your graph.

ehild
 
Ok when I tried to find the area using the graph i only took the area of the triangle.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

How to verify the Energy delivered by Lithium ion battery?
Replies
6
Views
2K
How much power is delivered to a circuit by a battery?
Replies
4
Views
4K
Battery Problem, Power delivered ,energy dissipated
Replies
2
Views
10K
How to Determine Power Output and Energy Storage Over Time?
Replies
12
Views
3K
How Much Air Does a 600W Hair Dryer Circulate Per Second?
Replies
6
Views
6K
How Do You Calculate Energy Delivered to an Inductor Over Time?
Replies
1
Views
2K
How much internal energy is produced in the battery
Replies
2
Views
6K
How much energy does the headlight use in 1.5 hours?
Replies
3
Views
4K
How Does Energy Dissipate in an LR Circuit with a 10V Battery?
Replies
9
Views
12K
How Do You Calculate Charge and Energy from Power and Voltage Over Time?
Replies
9
Views
4K

Hot Threads

Recent Insights

Back
Top