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.
