In practice, capacitance is usually a variable that depends on the materials and nearby objects and on the proximity to earth. Objects move around in daily life, and so their capacitance changes.
As an example, we can consider the human body. It is, in electrostatic terms, a conducting object, being mainly composed of water, which is a conducting material. Even if we neglect the nearby objects and earth, the human body can be approximated as a sphere that has a similar surface area. The “free space” capacitance of a sphere is given by 4πɛ0r, where r is the radius and ɛ0 is the permittivity of free space, 8.8 × 10−12 Fm−1. Typically, a 1 m radius sphere gives a useful approximation and has a “free space” capacitance around 110 pF.
Figure 2.2 Parallel plate capacitor.
Nearby objects and earth increase this value. In fact, the human feet, on the earth, approximate two parallel plate capacitors in parallel with the free space capacitance. Each capacitor is made up of two electrodes: the sole of the foot and the earth. These are separated by a layer of material (the shoe sole, typically an insulating polymer of relative permittivity ɛr around 2.5). Each foot capacitance varies from moment to moment as the feet are lifted and replaced on the ground during walking. Each foot capacitance can be modeled as a parallel plate capacitor (Figure 2.2), with plates of area A separated by a distance d and capacitance C given by
In general, if either the area A or the distance of separation d are changed, then the capacitance will change. If the charge is held constant, increasing the capacitance will decrease the body voltage, and reducing capacitance will increase body voltage. Reducing capacitance can be achieved by reducing the area (e.g. standing on tip‐toe) or increasing the separation distance (e.g. raising the foot from the floor).
The previous equation shows that if the charge on conductor is unchanged and the capacitance changes, then the voltage of the conductor changes. For example, if a person's body capacitance changes between 50 and 150 pF while walking and the charge on their body is constant at 5 nC, their body voltage will vary between 100 V (at 50 pF) and 33 V (at 150 pF). If a printed circuit board (PCB) conductor has a capacitance of 20 pF and charge 5 nC when resting close to a large earthed machine part, its voltage will be 250 V. If its capacitance is reduced to 5 pF when far away from this machine part, its voltage will rise to 1000 V.
It can be useful to have an idea of the approximate capacitance of everyday objects, especially when estimating the possible effect of ESD to or from such items. Table 2.2 gives some examples (IEC 61340‐1).
The variable ratio between charge and voltage behaves similarly for nonconductors.
When seated in a chair, the body generates charge on the clothes surfaces in contact with the chair. This forms a large area of charged material with a small distance between the charges (the two surfaces are in contact). The person's body voltage is low in this situation even though their clothing may be highly charged. On rising from the chair, the person can take much of the separated charge with them. The effective “capacitance” between the body and the chair is rapidly reduced (separation is rapidly increased), and a high body voltage quickly results if the charge cannot dissipate to ground. It is common to feel a shock on touching something metal after rising from a chair or car seat – voltages over 10 kV have been measured on people after getting out of a car seat (Pirici et al. 2003; Andersson et al. 2014).
Table 2.2 Approximate capacitance of typical everyday objects.
| Electronic components and small assemblies | 0.1–30 pF |
| Drinks can, small metal parts | 10–20 pF |
| Tweezers held in hand | 25 pF |
| Small metal containers (1–50 l), trolleys | 10–100 pF |
| Larger metal containers (250–500 l) | 50–300 pF |
| Human body | 100–300 pF |
| Small signal MOSFET gate capacitance | 100 pF |
| Power MOSFET gate‐source capacitance | 900–1200 pF |
| Car | 800–1200 pF |
MOSFET, Metal Oxide Silicon Field Effect Transistor
A corollary of this is that the voltage and field surrounding a charged object may be suppressed by the presence of a nearby conducting object. If the capacitance of the system is increased, the voltage is decreased.
As an example, a charged garment that fits snugly to the body has voltage suppressed due to the proximity of its surfaces to the body. Even if the garment is highly charged, the external field may be limited due to this. If the garment flaps open, the body and garment surfaces move apart. “Capacitance” is reduced, and a high voltage and electrostatic field appears outside the garment.
2.3.3 Charge Decay Time
The resistance and capacitance form a resistor‐capacitor (RC) network that has a characteristic time constant τ.
In a time τ, the voltage will decay to about 37% of its initial value.
In the example, if the charge current is suddenly halted at time t = 0 with initial voltage V0, the voltage V on the capacitor reduces as
An electrostatic field meter monitoring the material surface would measure this exponential decay of voltage. The product of a material's resistivity ρ and permittivity ɛ0 ɛr gives a physical time constant for the material.
This behavior has important practical implications. If we consider a situation in which the capacitance is fixed at 100 pF (the order of magnitude of capacitance of a person) and the charging current 100 nA, we can consider the effect of different resistances. With a resistance of 1 GΩ, the voltage generated is only 100 V, and on cessation of the current, the voltage will fall to 37% of its initial value within 109 × 10−10 = 0.1 seconds. The effect of a short duration charging current of this magnitude is unlikely to be noticed.
Figure 2.3 Charge or voltage decay