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Apple power supply consists of a very thick, inflexible AC cable (wall outlet to converter) and a very thin, flexible DC cable (converter to computer):

apple power supply

Why? The currents through the cables should be comparable, right?

EDIT: the label on the converter says:

  • input: 110-240V ~ 1.5A 50-60Hz
  • output: 16.5V = 3.65A max

EDIT2: cf. ThinkPad power adaptor (typical cables, similar to hp/dell &c)

ThinkPad power adaptor

Which has a thicker (than Apple) DC part and thinner (than Apple) AC part and is rated

  • input: 100-240V ~1.5A 50/60Hz
  • output: 20V =3.25A

The characteristics seem to be similar - why are the cables so dissimilar in the ratio DC cable thickness / AC cable thickness?

EDIT3: cf. AC Adapter For System76 Pangolin (which has 3 wires - including earth - in the AC part)

AC Adapter For System76 Pangolin

It is rated similar to the above and has a thicker DC part and thinner AC part than the Apple cable.

EDIT4: Looks like Lenovo/ThinkPad cables are under-engineered, which explains the cable thickness discrepancy observed!

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  • \$\begingroup\$ I have both a Thinkpad power supply from an X220 and an Apple power supply from a 2013 Macbook Pro. Diameters of the respective cables are almost identical. \$\endgroup\$ – Cybergibbons Jan 23 '14 at 22:57
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The size of the cables isn't due to the size of the copper conductor inside them - that's a fairly small part of the cable. Most of the bulk comes from the electrical insulation.

Electrical cable needs to be insulated so it doesn't short circuit. The higher the voltage, the thicker the insulation required.

Your thick mains power cord is insulated to withstand mains voltage. In your country, that's 110 VAC; in my country it's 230 VAC. On top of that, the insulation must withstand transient voltage spikes ("surges") - AS1660.3 specifies a multi-core flexible cable must withstand a 3,000V AC hi-pot test for five minutes, so the insulation must be thick enough to withstand 3,000V RMS or 4,200 V peak.

The thin DC cable, on the other hand, only has to withstand 12 VDC. There is not any chance of voltage spikes on this line because the design of the power supply won't allow them. There is minimal electrocution risk from 12 VDC. Therefore this cable doesn't need much insulation and it can be quite thin.

To emphasise the relationship between voltage and insulation thickness, you can get cables like this:

Big cable

The copper conductor is relatively small relative to the overall diameter of the cable. Note the thickness of the insulation (the white material). This short off-cut of cable had no markings, but this is rated for at least 132,000 VAC and the insulation is thicker to match.

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  • \$\begingroup\$ Are you saying that the thinkpad cables are too flimsy? \$\endgroup\$ – sds Nov 8 '13 at 4:51
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    \$\begingroup\$ The Thinkpad cable illustrated appears to have two pins, so it is a two core cable (active and neutral.) The Apple cable has three pins, so it is a two core and earth cable (active, neutral, earth.) The insulation thicknesses are probably similar, but the Apple cable has an entire extra core inside which explains the larger outer diameter. \$\endgroup\$ – Li-aung Yip Nov 8 '13 at 5:02
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    \$\begingroup\$ @sds - It's also worth noting that the cable profiles are different. The thinkpad power cable is a figure-eight in profile (cut & look end-on). The apple cable is round. If you draw the smallest circle with which you can encompass the thinkpad cable, it's still considerably larger in diameter. \$\endgroup\$ – Connor Wolf Nov 8 '13 at 8:38
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    \$\begingroup\$ I have to object here. The size of a power line cord is not dictated primarily by the voltage rating of the insulation. If this were the case, the 4-mil thick Kynar (dielectric strength 1.6 kV/mil) insulation used on wire-wrap wire should be adequate. A cable must be constructed rugged enough to withstand any foreseeable use or abuse that it could be subjected to in service. See for example UL 1581 or UL 2556. These standards specify endurance tests, such as crush resistance, impact resistance, mechanical strength, abrasion resistance, among others that cables are required to pass. \$\endgroup\$ – user28910 Nov 8 '13 at 16:12
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    \$\begingroup\$ Just a hunch here, but even though that mains plug uses the NEMA 5-15 Type B end (which is normally used for 115V systems) the actual cable is built to support 240V. In part because the corresponding socket is also in use in other, 240V countries to support travelers. (See: en.wikipedia.org/wiki/…). That ThinkPad's cable is likely designed to only support the N. American 115V market. \$\endgroup\$ – mkoistinen Nov 8 '13 at 16:52
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The current through the DC cable will in fact be several times the current through the AC cable (explanation follows in a bit), but the reason the AC cable is thicker is about operator safety, rather than current carrying capacity.

The mains wire has far thicker insulation (and purely incidentally, thicker conductor cross-section as well) to provide some additional safety in case of repeated bending, abrasion or impact, and resultant cable damage.

Basically, a person might get seriously harmed by contact with a conductor carrying mains voltage, if the conductor were to somehow be exposed due to insulation damage. With the DC wire, contact does not carry risk of electrocution, due to the lower voltage involved.


Estimation of Current:

The power through the mains wire will be the efficiency of the power convertor, times the power drawn on the DC side, plus a bit of overhead / quiescent power. So, if we assume a 110 Volt mains supply, 80% efficiency, negligible quiescent power and an output of 5 Volts DC supplying 5 Watts of power to the device, then:

  • P = V x I, thus DC current I = 5/5 = 1 Ampere
  • Power drawn on the AC side: 5 / 0.8 = 6.25 Watts
  • AC wire current I = 6.25/110 = 0.0568 Amperes = 58.6 mA

So it's certainly not about current carrying capacity on the AC side!

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  • \$\begingroup\$ I think it also has to do with the fact that in case of a fault you want the fuse in the power brick to melt, rather than the mains cable. Remember that in a fault condition a much higher current is possible than rated. \$\endgroup\$ – jippie Nov 8 '13 at 8:05
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    \$\begingroup\$ @jippie: nearly correct - you want the upstream fuse to melt before the cable does. The fuse in the power brick won't help you if the fault is on the cable itself. ;) \$\endgroup\$ – Li-aung Yip Nov 8 '13 at 14:44
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    \$\begingroup\$ @jippie though you are absolutely correct that cables are rated for fault withstand capability, just as much as current-carrying capacity and voltage drop. The Australian LV cable selection standard, AS3008.1, mandates that you consider all three of the above factors. \$\endgroup\$ – Li-aung Yip Nov 8 '13 at 14:50
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The current in the DC side is going to be much higher. But it's also limited by the power brick, and it's a much lower voltage. The AC cord needs to be thick because it has to be durable. Most of the thickness will be insulation.

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As it's an apple product the answer is probably design. It is designed to be as thin as possible and still fulfil the legal requirements.

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Actually, current would be lower in the AC cable. It probably has more to do with the durability (resistance to physical damage) requirements of the AC cable which is carrying higher line voltage.

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UL requirements apply, in particular, to the AC side of the power adaptor, and specify a specific set or requirements that must be met for any cable that conducts AC household voltages. Apple made that cable as thin as possible while still meeting all those conditions - current handling capability, insulation, high potential arcs and faults, and physical durability, including cut, heat, flex, and wear resistance.

If the only requirements were to withstand 120VAC RMS without arcing, and conduct up to 1 amp, they could have made it much, much thinner.

UL requirements are quite rigorous.

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There are four constraints on the minimum size of the dc cable:

  1. rated voltage
  2. rated current
  3. degradation rating (over the life of the product we expect it to lose no more than x% voltage/current carrying capacity due to wear and tear/abuse)
  4. cable availability

There are four constraints on the minimum size of the ac cable, and here is the shocker, they are exactly the same four constraints. The differences are entirely in the voltage and current ratings. In both cases the cable must be sized by the power source. In the dc case the source is the power supply (which is in turn sized by the load). In the ac case the source is the outlet. By strict interpretation of the NEC the outlet can supply 20 amps at 115 volts, although since the power supply is rated for 220 volts you must assume that the cable will be plugged into an adapter plug and there are installations that put 20 amp outlets on 30 amp circuits (jails and schools like to do this). So the cord should be able to handle a failure at 220 volt 30 amp.

I have never seen wire rated for either 110 volt or 220 volt. 300 volt and 600 volt cable is common. Typically they use 300 volt cable for low voltage wiring and 600 volt for the ac side. 14 gauge wire can carry 20 amps, although it may get warm doing so, and will probably not fail under a 30 amp surge.

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The size of flexible mains cables for small devices is determined mainly by safety considerations. The cores must be thick enough not to break from mechanical stresses and thick enough that in the unlikely event of a short circuit they don't vaporise before the fuse/breaker does. The insulation and sheath must be thick enough that even after many years of wear and tear they still provide adequate insulation.

The apple cable has an earth wire (even though strangely the adaptor peices that allow you to use the power brick without the cable are unearthed). An earth wire is desirable on larger switched mode power supplies because it allows touch currents to be dramatically reduced.

I suspect the weird connector has an influence too. Apple may not want to design variants of that connector for different cable types and may instead have chosen to go for a type/size that would be acceptable everywhere. Cloverleaf cables on the other hand are made in massive quantities, so it makes more sense to design variants for each countries specs and the commoditisatoin provides much more scope for dodgy vendors in china to push out noncompliant product.

The DC output cable on the other hand is not considered a significant safety risk, so it's size is mostly down to the vendors compromise between efficiency and good looks. Apple wants their machines to look sleek in the store, so thin cable it is.

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