Building a 6 V, 0.1 A Source from 1.5 V Dry Cells

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Electric Circuits Intermediate Ohm's Law

Source: High school physics (Chinese)

Problem Sets:

ohm's law

Problem

Each dry cell has an EMF of $1.5 \ \text{V}$ and the maximum current it can safely supply is $0.05 \ \text{A}$.

A power source with EMF $6 \ \text{V}$ and maximum current $0.1 \ \text{A}$ is required. How should the dry cells be combined to obtain it?

Use $8$ cells arranged as $2$ parallel branches of $4$ series cells each.

Cells in series add EMFs but keep the same current limit; cells in parallel keep the EMF but add current capacities.

To reach $6 \ \text{V}$: connect $n = 6/1.5 = 4$ cells in series. Such a string still has a current limit of only $0.05 \ \text{A}$.

To reach $0.1 \ \text{A}$: put $m = 0.1/0.05 = 2$ such strings in parallel.

Total cells: $n \times m = 4 \times 2 = 8$. Arrangement: $2$ parallel branches, each consisting of $4$ cells in series.