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Chapter 5

Q. 5.12

Explosive Atmosphere

When working in a hazardous, explosive atmosphere, workers must ensure that equipment does not produce any sparks that may lead to an explosion. At a minimum, any sparks must be isolated from the surrounding environment. Chapter 15 outlines how even a simple flashlight can create potentially dangerous sparks.

A standard flashlight circuit is shown in Figure 5.32. A flashlight bulb consists of both a resistance and an inductance. To illustrate the spark hazard, find the voltage across the switch at time t=0^+.

5.12

Step-by-Step

Verified Solution

Before opening the switch (i.e., t < 0), the circuit can be modeled as shown in Figure 5.33 (a). Because the switch has been closed for a long time period, the inductor functions similar to a short circuit. Replacing the inductor with a short circuit in Figure 5.33 (a), the current flowing through the resistor corresponds to:

i(t)=\frac{3}{5}=0.6

As stated earlier, the current through the inductor cannot change suddenly. Therefore:

i_{L}\left(0^{+}\right)=i_L\left(0^{-}\right)=0.6  A

The resistance of an open circuit is infinity. However, at the time of opening the switch, the air between the two closely located switch contacts may be modeled as a finite resistance, R_{\text {switch }}. Therefore, the 0.6 A current through the air \left(R_{\text {switch }}\right) may create a spark.

The voltage across the switch is:

v_{\text {switch}}(t)=R_{\text {switch}} \cdot i(t)

If R_{\text {switch }} tends to infinity, v_{\text {switch }} also will tend to infinity. This can produce a spark. As discussed in Chapter 15, if hazardous materials are located close to the spark it may create an explosion.

5.12-