• Pixel-art sticker of Saggo, personifying Internal Resistance, with the caption “Draw More, Drop More.”

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Saggo

Internal Resistance Physics

\[V = \varepsilon - I r\]
$4.99 USD
$4.99 USD
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Meet Saggo, a battery who sags a little with every bulb he lights. Internal resistance eats part of his push, so terminal voltage is the emf minus current times internal resistance. A 12.6 V car battery feeding a 150 A starter drops to about 9.6 V. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Saggo, a battery who sags a little more with every bulb he has to light.

Every real battery has some internal resistance, r, inside its chemistry and connections. When current flows, part of the battery's push is used up just driving current through itself. So the voltage at the terminals is less than the battery's emf, ε, the voltage it shows when no current flows.

The terminal voltage is V = ε − Ir. A car battery with ε = 12.6 V and r = 0.02 Ω feeds a starter motor drawing 150 A. The drop is Ir = 3 V, so the terminals sit at only about 9.6 V.

That is why headlights dim while the engine cranks. With a light load of 5 A the drop is just 0.1 V.

Internal resistance rises as batteries get cold or old, which is why a weak battery often fails on a winter morning. The power lost inside, I²r, also warms the battery while it works hard.

Equations

\[V = \varepsilon - I r\]
SymbolMeaningUnit
\(V\) terminal voltage \(\mathrm{V}\)
\(\varepsilon\) emf of the battery \(\mathrm{V}\)
\(I\) current drawn \(\mathrm{A}\)
\(r\) internal resistance \(\mathrm{Ω}\)

Sources

  1. OpenStax University Physics Vol. 2 — Electromotive Force
  2. Wikipedia — Internal resistance

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