AC Electric Circuits

Mutual Inductance

12 questions By Tony R. Kuphaldt

PDF Version

Page 2 of 4 0 of 12 answers revealed (0%)

Question 4 of 12

Write the equation describing the voltage induced in this coil, solving for (instantaneous) induced voltage (e) in terms of the instantaneous magnetic flux (φ) and the number of turns of wire in the coil:

Reveal answer

e = N\(\frac{dφ}{dt}\)

Follow-up question: algebraically manipulate this equation to solve for the number of turns (N) given all the other quantities.

Notes:
It should be noted that in this particular case, N is equal to three (counting the turns in the illustrated coil).
Question 5 of 12

There are two wire windings wrapped around a common iron bar in this illustration, such that whatever magnetic flux may be produced by one winding is fully shared by the other winding:

Write two equations describing the induced voltage at each winding (e_p = ... and e_s = ...), in each case expressing the induced voltage in terms of the instantaneous magnetic flux (φ) and the number of turns of wire in that winding (N_p and N_s, respectively).

Then, combine these two equations, based on the fact that the magnetic flux is equal for each winding.

Reveal answer

e_p = N_p dφ
dt

e_s = N_s dφ
dt

Then, combining the two equations:

e_p
N_p = e_s
N_s

Notes:
Obtaining the last equation is an application of the mathematical truth that quantities equal to the same thing are equal to each other (if a = c and b = c, then a = b).
Question 6 of 12

There are two wire windings wrapped around a common iron bar in this illustration, such that whatever magnetic flux may be produced by one winding is fully shared by the other winding:

Write two equations describing the induced voltage at each winding (e_p = ... and e_s = ...), in each case expressing the induced voltage in terms of the instantaneous current through that winding (i_p and i_s, respectively) and the inductance of each winding (L_p and L_s, respectively).

We know that the induced voltages in the two windings are related to each other by this equation, if there is perfect “coupling” of magnetic flux between the two windings:

e_p
N_p = e_s
N_s

Knowing this, write two more equations describing induced voltage, this time expressing the induced voltage in each winding in terms of the instantaneous current in the other winding. In other words,

e_p = ... i_s

e_s = ... i_p

Reveal answer

Equations describing self-inductance:

e_p = L_p di_p
dt

e_s = L_s di_s
dt

Equations describing inductance from one winding to the other:

e_p = L_s N_p
N_s di_s
dt

e_s = L_p N_s
N_p di_p
dt

Notes:
The first two equations are mere review. The second two equations require algebraic manipulation and substitution between equations.