All Problems

Electric Oscillations

Problem 4.116

There are two oscillating circuits (Fig. 4.31) with capacitors of equal capacitances. How must inductances and active resistances of the coils be interrelated for the frequencies and damping of free oscillations in both circuits to be equal? The mutual inductance of coils in the left circuit is negligible.

Reveal Answer
1L1+1L2=1L and 1R1+1R2=1R\frac{1}{L_{1}}+\frac{1}{L_{2}}=\frac{1}{L} \text { and } \frac{1}{R_{1}}+\frac{1}{R_{2}}=\frac{1}{R}