What is the coefficient of coupling - assume that the

Question

The next problem(s) addresses the following course learning objective(s):

- Understand the dot convention for magnetically coupled circuits.
- Analyze magnetically coupled circuits.

1. Problem 1. (The circuit of Example of 6.6 is shown below as well)

a) Write a set of mesh-current equations for the circuit in Example 6.6 if the dot on the 4 H inductor is at the right-hand terminal. the reference direction of i_g is reversed, and the 60Ω resistor is increased to 780Ω.
h) Verify that if there is no energy stored in the circuit at t = 0, and if i_g = 1.96 - 1.96e^-41 A, the solutions to the differential equations derived in (a) of this Assessment Problem are

i₁ = -0.4 - 11.6e^-4t + 12e^-5t A.

i₂ = -0.01 - 0.99e^-4t + e^-5t A.

2. Problem 2

Two magnetically coupled coils have self-inductances of 52 mH and 13 mH, respectively. The mutual induc¬tance between the coils is 19.5 mH.

a) What is the coefficient of coupling?

b) For these two coils, what is the largest value that M can have?

c) Assume that the physical structure of these cou-pled coils is such that ρ₁ = ρ₂. What is the turns ratio N₁/N₂ if N1 is the number of turns on the 52 mH coil?

3. Problem 3

The self-inductances of the coils in Fig. 6.30 given below are L₁ = 25 [mH] and L₂ = 100 [mH]. If the coefficient of coupling is 1.0, then do the following problems.

a) If i₁ equals 10 A, what value of i₂ results in zero stored energy?

b) Is there any physically realizable value of i2 that can make the stored energy negative?

Figure 6.30 The circuit used to derive the basic energy relationships.

The next problem(s) addresses the following course learning objective(s):
- Understand linear transformer and ideal transformer.
- Analyze transformer circuits.

4. Problem 4

A linear transformer couples a load consisting of a 360 Ω resistor in series with a 0.25 H inductor to a sinusoidal voltage source, as shown. The voltage source has an internal impedance of 184 + J0 Ω ft and a maximum voltage of 245.20 V, and it is operating at 800 rad/s. The transformer parameters are R₁ = 100 it, L₁ = 0.5 H, R₂ = 40 Ω, L2 = 0.125 H, and k = 0.4. Calculate (a) the reflected impedance; (b) the primary current; and (c) the secondary current.

5. Problem 5

The source voltage in the phasor domain circuit in the accompanying figure is 25∠0^o kV. Find the amplitude and phase angle of V₂ and I₂.

6. Problem 6

a) Find the steady-state expressions for the cut rents i_g and i_L in the circuit in Fig. P9.72 which v_g = 200 cos 10,000t V.

b) Find the coefficient of coupling.

c) Find the energy stored in the magnetically coupled coils at t = 50Π μs and t = 100Π μs

7. Problem 7

Find the impedance Z_ab in the circuit in Fig. P9.77 if Z_L = 200 + j1.50 Ω.

Figure P9.77