# RLC Series Circuit

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## Exercises with Solutions

Use this formula eBook if you have problems with physics problems.

### Exercise #1: Electric Spark Suppression with Capacitor (Snubber)

When the current flowing through the coil is switched off by a switch, a high voltage is momentarily generated at the switch, leading to an electric spark.

The coil has an inductance $$L = 4.2 \, \text{H}$$ and a current flows through it $$I = 1 \, \text{A}$$. To eliminate the arc at the switch, a capacitor is connected in parallel to the coil, which can withstand a maximum of $$500 \, \text{V}$$.

What capacity $$C$$ must the capacitor have for this?

#### Solution to Exercise #1

The induction voltage at the coil is given by: $U ~=~ L \, \frac{dI}{dt}$

In this case, you can write: $U ~=~ L \, \frac{I}{\Delta t}$

Capacitance of a capacitor is: $C ~=~ \frac{Q}{U}$ where charge is given by $$Q ~=~ I \, t$$: $C ~=~ \frac{I\Delta t}{U}$

Rearrange for time: $\Delta t ~=~ \frac{L\,I}{U}$

Substitute into equation for $$C$$: $C ~=~ \frac{I^2 L}{U^2}$

Thus, the capacitance is: $C ~=~ 1.68 \,\cdot\, 10^{-5} \, \text{F} ~=~ 16.8 \, \mu\text{F}$

Alternatively, the conservation of energy $$\frac{1}{2}\,C\,U^2 = \frac{1}{2}\,L\,I^2$$ can be utilized.