Question

A container of value 1.0uF is charged at 50 volts. What is the value of the induction coil connected to both ends of the coil holder when the maximum current in the coil is 0.5 amperes?

Answer 1

There is no energy dissipates in the LC-circuit. Therefore, the maximum energy stored in the capacitor is equal to the maximum energy stored in the inductor:

$$E_{C_{max}}=E_{L_{max}},$$ $$\dfrac{1}{2}CV^2=\dfrac{1}{2}LI_{max}^2,$$ $$L=\dfrac{CV^2}{I_{max}^2}=\dfrac{1.0\cdot10^{-6}\ F \cdot(50\ V)^2}{(0.5\ A)^2}=0.01\ H.$$