Question

N=350 turns

I=0.42 A
Φ= 8.5
I1=1.26 A
Δt=4.5 seconds
Part (a) Express the inductance L in terms of N, I and Φ.
Part (b) Calculate the numerical value of L in H.
Part (c) Express the magnitude of the induced emf in terms of L, I, I1, and Δt.

Answer 1

The inductance L can be expressed as L = NΦ/I. When calculated with provided values, L equals 7.083 H. The magnitude of induced emf is given by emf = -L(ΔI/Δt).

To express the inductance L in terms of N, I, and Φ, use the formula L = NΦ/I, derived from the equation of self-inductance L = NΦm/I where Φm is the magnetic flux.

For part (b), substitute the given values into the formula: L = NΦ/I = (350 turns × 8.5 Wb) / 0.42 A. This calculation yields L = 7083.33 Wb/A, or 7.083 H, since 1 Wb/A is equal to 1 H (Henry).

For part (c), to find the magnitude of the induced emf, use Faraday's Law of Induction, which states that the emf induced in a circuit is equal to the negative change in magnetic flux times the number of turns per unit time, or emf = -L( ΔI/Δ1t), where ΔI is the change in current and Δ1t is the change in time.

Answer 2

For Part (a) : L = N * ( Ф / I )

For Part (b) : 7083.33 H

For Part (c) : ε = L( ( I1 - I ) / Δt )

Step-by-step explanation:

Part (a) is simply asking if you know the definition of inductance. We know that inductance of a single turn/loop is the magnetic flux threading the turn/loop divded by the current in the turn/loop ( ( Ф / I ) ) . Since you are being asked to find the total inductance of the inductor, you would multiply the inductance of a single turn/loop by the number of turns/loops ( N ). This means that you should get the equation

L = N * ( Ф / I )

Part (b) is plugging in the given numbers into the equation that you expressed in Part (a)

To do so,

L = N * ( Ф / I ) = 350 (turns) * ( 8.5 T·m² / 0.42A ) = 7083.33 H

For reference:

One Tesla (T) is equal to 1 kg / ( s² * A )

One Henry (H) is equal to 1 ( kg * m² ) / ( s² * A² )

*Note that turns is not a unit that is part of the final unit of Henrys, it simply acts as a coeffecient for our purposes.

Part (c) once again asks for you to demonstrate a basic memory of the equation/definition of induced emf (ε). Induced emf is always proprtional to the time rate of change of the current ( ( I1 - I ) / Δt ). This is to say that the induced emf is proprtional to the magnetic flux which is proportional to the magnetic field which is itself proportional to the current. The inductance of the inductor (L) is a constant of proportionality for the induced emf, and thus the time rate of change of the current is multiplied by the inductance of the coil. Thus,

ε = L( ( I1 - I ) / Δt )