Question

An ideal solenoid with 875 turns is 0.250 m long and has a cross-sectional area of 3.00 ✕ 10⁻³ m².

(a) What is the inductance of this solenoid?
H

(b) If we connect this solenoid in series with a 12.0-V battery and a 195-Ω resistor, what is the maximum value of the current?
A

(c) Assuming the current is zero when t = 0 as the circuit elements are connected, at what time will the current reach 50% of its maximum value?

s

Answer 1

inductance = * N² * A / length

= 4pi*10^-7  *  875² * 3.00 ✕ 10^-3  m²  / 0.250

L = 0.011545353

(b ) max value of current will be at very longg time because inducter behave like wire after long time so simply max current =

i = V / R = 12/ 195 = 0.06153846154 A

(c)

I = I₀ * (1- e^{-t*R / L}  )

we want I = 0.5 I₀   so   

0.5 I₀    = I₀ * (1- e^{-t*R / L}  )

0.5 = 1- e^{-t*R / L}

e^{-t*R / L}    = 0.5

take log both side

-t*R / L = ln 0.5

t = - (L/R ) *ln 0.5

we alredy ahve L and R put them here we got

t= 4.1 *10^-5  sec