Do longer wires consume more power?

Question

In DC, for example at 12V, will a longer power wire (lets say 10 meters vs 10 centimeters) cause a high current consumption?

Answer 1

Power can be expressed as \$P = IV\$. We also know that Ohms law says \$V = IR\$. Putting these two together, we get the expression:

$$P = \frac{V^2}{R}$$

In your case you have a fixed voltage source - so \$V=12\mathrm{V}\$. Put that in to the equation we get:

$$P = \frac{12^2}{R} = \frac{144}{R} = \frac{144}{R_{wire}+R_{load}}$$

As your wire gets longer, the resistance of it increases. As a result, the total power dissipated in the entire circuit is going to decrease. The power dissipated in the wire itself may go up, or it may go down.

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How the current is affected will depend on what the circuit is. For example if you have a simple resistive load, then from ohms law we can find out how the current will be affected:

$$I = \frac{V}{R} = \frac{12}{R_{wire} + R_{load}}$$

If you increase the wire resistance, the total current will decrease. Depending on the ratio between wire resistance and load resistance, the power dissipated in the wire itself may go up, or it may go down.

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However, if your load was, say, a constant current load, then things get a little more tricky. So long as there is enough voltage across the load to maintain the constant current, then we can say for sure that the power dissipated in the wire will increase. Going back to the first two equations, we can also derive that power is:

$$P = I^2R$$

So if the current stays the same, but the resistance of the wire is increased, then the power dissipated in the wire is going to be larger.

Answer 2

A real example of where a longer wire will cause greater current consumption is a switching DC to DC converter - it may work across a range of input voltages such as 5V to 20V to produce a constant (say) 10V on the output.

When it is fed from 20V and the final load is (say) 10 ohms, the power demand is 10 watts (100 % efficiency) and this will therefore take 0.5 amps from the 20V supply. However if the converter feed cable resistance became significant, the voltage at the converter's input terminals would reduce and, to maintain 10 watts into the load, a current greater than 0.5 amps is required to flow down the cable. As the cable got longer more current would be required and taking this to it's natural conclusion, eventually the cable resistance would not be able to support 5V at the input to the converter and the converter output would begin to fall-off.

So yes, there are circumstances when a longer cable causes more current flow.