Question

Problem 2: (50 points) For the system shown in Fig. 2: W NI N2 PEN Fig. 2 Voltmeter (very large impedance) N? = 200 N? = 150 Table 2: Transformer Parameters N = 100 A, = 0.002 m² (cross sectional area) 1, = 0.128 m (mean length of mate- rial) ?, = 2000 4. = 4?. 10?? ?. = 0.5 ? 12 = 0.5 ? Wb/A*m a) Derive the T-equivalent circuit between winding 1 and winding 2 (note the direction of flux produced by winding 1 and winding 2 oppose each other). Ignore leakage inductance L1, L2, and L3. (25 points) b) Find the mutual inductance L12, L13, and L23. (15 points) c) Given the following input currents on windings 1 and 2 of the transformer given above. Find the voltage seen at the voltmeter (V3 =?). (10 points) 1? = sin(2?t) 12 = (-4/3)sin(2?t)

          Problem 2: (50 points)
For the system shown in Fig. 2:
W
NI
N2
PEN
Fig. 2
Voltmeter
(very large
impedance)
N? = 200
N? = 150
Table 2: Transformer Parameters
N = 100
A, = 0.002 m²
(cross sectional
area)
1, = 0.128 m
(mean length of mate-
rial)
?, = 2000
4. = 4?. 10??
?. = 0.5 ?
12 = 0.5 ?
Wb/A*m
a) Derive the T-equivalent circuit between winding 1 and winding 2 (note the direction
of flux produced by winding 1 and winding 2 oppose each other). Ignore leakage
inductance L1, L2, and L3. (25 points)
b) Find the mutual inductance L12, L13, and L23. (15 points)
c) Given the following input currents on windings 1 and 2 of the transformer given
above. Find the voltage seen at the voltmeter (V3 =?). (10 points)
1? = sin(2?t)
12 = (-4/3)sin(2?t)

Problem 2: (50 points)
For the system shown in Fig. 2:
W
NI
N2
PEN
Fig. 2
Voltmeter
(very large
impedance)
N? = 200
N? = 150
Table 2: Transformer Parameters
N = 100
A, = 0.002 m²
(cross sectional
area)
1, = 0.128 m
(mean length of mate-
rial)
?, = 2000
4. = 4?. 10??
?. = 0.5 ?
12 = 0.5 ?
Wb/A*m
a) Derive the T-equivalent circuit between winding 1 and winding 2 (note the direction
of flux produced by winding 1 and winding 2 oppose each other). Ignore leakage
inductance L1, L2, and L3. (25 points)
b) Find the mutual inductance L12, L13, and L23. (15 points)
c) Given the following input currents on windings 1 and 2 of the transformer given
above. Find the voltage seen at the voltmeter (V3 =?). (10 points)
1? = sin(2?t)
12 = (-4/3)sin(2?t)

Added by Kelly F.

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