# RLC Series Circuit

## 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.