Optimizing Battery Connections: A Scientific Approach

[banoosh]

Homework Statement

Suppose you have two “D” cells and wish to use them to power a light bulb.

The two batteries can either be connected in series or in parallel.
(a) In order to achieve maximum voltage, how should the cells be connected? Explain.
(b) In order to achieve maximum power, how should the cells be connected? Explain.
(c) In order to last longest before going dead, how should the cells be connected? Explain.
(d) How many times longer will the cells last when connected this way versus the other? Explain.

Homework Equations

P= IV
V= IR
Req= r1+r2+...
1/Req= 1/r1 + 1/r2 + ...

The Attempt at a Solution

Having some trouble grappling with conceptuality here. how do the two types of series differ in functionality? i know what series and parallel circuits look like but not how they work. any help is appreciated

 

[TomHart]

What is the equivalent voltage of two batteries of, say, 1.5 volts each connected in parallel?
What is the equivalent voltage of those same two batteries connected in series?
What circuit component represents the light bulb?
Can you draw a simple circuit diagram of those two configurations - batteries in parallel powering the bulb, and batteries in series powering the bulb?

 

[CWatters]

P= IV
V= IR

Try substituting to get an equation for P in terms of V and R.