# Ohms

**Ohms** are a measure of the resistance to a flow of current. The name derives from the German physicist Georg Simon Ohm (1759-1854). The symbol for the ohm is the Greek capital letter omega. If the Greek letter cannot be used, the word *ohm* is used instead.

In a simple circuit the relationship between the current-forcing potential (V, Volts), the current flowing (confusingly written as I, but measured in Amps) and the resistance (R, ohms) is V = IR or Ohm’s Law.

For DC circuits the sums are simple. P48 Phantom Power is fed via two parallel 6800 ohm resistors – a combined value of 3400 Ohms. If a microphone is specified to draw 4mA of current the voltage across the microphone will be:

V = 3400 ohms x 0.004 A = 13.6 V

The P48 supply will therefore be reduced to 48 – 13.6 = 34.4 V at the connecting XLR.

Resistance is similar in concept to friction and a current forced through a resistance will generate heat. Resistance is not constant with temperature so the filament of a lamp has a very different resistance when hot than when cold. Calculations of resistance can be confused by this effect.

The relationship of Ohm’s Law means that wherever there is a current flowing through a resistor there will always be a voltage detectable across it. Good conductors will have a very small voltage difference, while insulators will have very large ones.

**Ohms in AC circuits**

Resistance also impedes AC but in this case the situation is complicated because circuit elements not only have simple resistance (which doesn’t change with frequency) but also Inductance and Capacitance, which are frequency dependent. This complex “resistance” is termed Impedance but is still measured in ohms and can be calculated in the same way as long as you remember that the results only work for particular frequencies.

In many cases in audio, impedances are arranged to minimise the effects of frequency dependence, in which case impedances can be treated as if they were simple resistance.

Cable connections are usually fed from a low impedance source (hence able to supply current easily) but “listened to” by a high impedance load (10 – 20 kilohms). As with simple resistances a large voltage will be detectable across the large impedance. By comparison the connecting cable will have a very low impedance, at useful frequencies, thus its effect can be ignored.

Characteristic Impedance of cables and connectors is a matter of Transmission Line theory.

**Scale**

Connectors should have contact resistances in the range of millohms (1/1000ths of an ohm).

Loudspeaker amp outputs have a source impedance of <0.1 ohms and the speaker load is in the range of 4 – 16 ohms.Ω

Loudspeaker cable must carry high currents – its resistance is typically 30 – 40 millohms (10^{-6} ohms) per 10m.

Headphones are typically 30 – 80 ohms impedance, although ‘high impedance’ types are also available and in common use, at around 2000 ohms.

Chunky microphone cable has a resistance of 0.4– 0.5 ohms per 10m. Lighter cables may be 1 ohm per 10m.

Insulators have a resistance measured in megohms (10^{6} Ohms)or gigohms (10^{9} ohms).

Low impedance audio signal sources are 30 – 150 ohms.

High impedance loads vary from 1.2 – 2.5 kilohms for low-level microphones to 10 – 20 kilohms for high-level lines.

Electric guitar pickups need load impedances in the range of 100 kilohms – 1 megohm.Ω