Question

The energy in an oscillating LC circuit containing a 1.57 H inductor is 5.76 μJ. The maximum charge on the capacitor is 201 μC. For a mechanical system with the same period, find the

(a) mass
(b) spring constant
(c) maximum displacement
(d) maximum speed.

Answer 1

(a)1.57 kg

(b) 281.17 N/m

(c) 201 micrometer

(d)
`2.69* 10^(-3)m/sec`

Step-by-step explanation:

We have given that value of inductor L = 1.57 Henry

Inductive energy
`E=5.76\mu j=5.76* 10^(-6)J`

Maximum charge
`Q=201\mu C=201* 10^(-6)C`

(A) In electrical mechanical system mass corresponds to inductance

So mass will be m = 1.57 kg

(B) We have given energy
`E=(Q^2)/(2C)`

`C=(Q^2)/(2E)=((201* 10^(-6))^2)/(2* 5.7* 10^(-6))=3543.94* 10^(-6)`

In electrical mechanical system spring constant is equivalent to
`(1)/(C)`

So spring constant
`k=(1)/(C)=(1)/(3543.94* 10^(-6))=282.17N/m`

(c) Displacement is equivalent to maximum charge

So displacement will be
`x=201\mu m`

(d) Maximum speed is correspond to maximum current

As maximum current
`i_m=(Q)/(√(LC))=\frac{201* 10^(-6)}{\sqrt{1.57* 3543.94* 10^(-6)}}=2.69* 10^(-3)A=2.69* 10^(-3)m/sec`