Question

An inductor is energized as in the circuit of Fig. 2-4a. The circuit has L 10 mH and VCC 14 V. (a) Determine the required on time of the switch such that the peak energy stored in the inductor is 1.2 J. (b) Select a value for R such that the switching cycle can be repeated every 20 ms. Assume the switch and the diode are ideal.

Answer 1

Answer:

A) 11.1 ms

B) 5.62 Ω

Explanation:

L ( inductance ) = 10 mH

Vcc = 14V

A) determine the required on time of the switch such that the peak energy stored in the inductor is 1.2J

first calculate for the current  ( i )  using the equation for energy stored in an inductor hence

i = $\sqrt{\frac{2W}{L} }$   ----- ( 1 )

where : W = 1.2j ,  L = 10 mH

Input values into equation 1  

i = 15.49 A

Now determine the time required  with expression below

i( t ) = 15.49 A

L = 10 mH, Vcc = 14

hence the time required ( T-on ) = 11.1 ms

attached below is detailed solution

B) select the value of R such that switching cycle can be repeated every 20 ms

using the expression below

τ = $\frac{L}{R}$  ---- ( 2 )

but first we will determine the value of τ

τ = t-off / 5 time constants

  = (20 - 11.1 ) / 5  = 1.78 ms

Back to equation 2

R = L / τ

  = (10 * 10^-3) / (1.78 * 10^-3)

  = 5.62 Ω