Physics Generator Questions

Question

A generator is to be connected in series with an inductor of L= 2.50 mH and a capactiance C. You are to produce C by using two capacitors of capacitance 2.00 micro-F and 3.00 mirco-F either singly or together. What resonant frequencies can the circuit have depending on the value of C?

There are four answers.

Answer 1

For a series resonant circuit, f = 1 / [ 2π √ (LC) ].

There are four possibilities:

1.  L and C1, in series:

►  f = 1 / [ 2π √ (2.5 E-3 × 2 E-6) ] = 2 251 Hz = 2.251 kHz.

2.  L and C2, in series:

►  f = 1 / [ 2π √ (2.5 E-3 × 3 E-6) ] = 1 838 Hz = 1.838 kHz.

3.  L in series with (C1 in parallel with C2) (capacitances just add):

►  f = 1 / [ 2π √ (2.5 E-3 × 5 E-6) ] = 1 424 Hz = 1.424 kHz.

4.  L in series with (C1 and C2 in series) [Ceq = 1 / (1/C1 + 1/C2) = 1 / (1/2 + 1/3) = 1 / 5/6 = 6/5 = 1.2 µF]

►  f = 1 / [ 2π √ (2.5 E-3 × 1.2 E-6) ] = 2 906 Hz = 2.906 kHz.