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## 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 $t=0^+$.

## 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.