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Drill Exercise 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 and a maximum voltage of 245.20 V, and it is operating at 800 rad/s. The transformer parameters are R1 = 100Ω, L1 = 0.5 H, R2 = 40Ω, L2 = 0.125 H, and k = 0.4. Calculate : a). The reflected impedance, b). The primary current, c). The secondary current, and d). The average power delivered to the primary terminals of the transformer. Ideal Transformer Example 4:1 ideal 60Ω 50 0 A rms 40Ω 20Ω a). Find the average power delivered by the sinusoidal current source in the circuit shown. b). Find the average power delivered to the 20 Ω resistor. 60Ω + 4:1 V1 - + 3000 0 V rms V2 ideal 40Ω i1 20Ω Solution a). + i2 300 60 I1 V1 20I1 I 2 0 20I 2 I1 V2 40 I 2 V2 14 V1 I 2 4I1 The solutions for V1, V2, I1 and I2 are V1 260 V rms V2 65 V rms I1 0.25 A rms I 2 1.0 A rms The voltage across the 5 A current source is V5 A V1 20I1 I 2 260 200.25 1 285 V rms The average power associated with the current source is P 2855 1425 W b). To find the average power delivered to the 20Ω resistor I 20 I1 I 2 0.25 1 1.25 A rms P20 1.25 20 31.25 W 2 Drill Exercise Find the average power delivered to the 4 kΩ resistor in circuit shown. 10Ω 1:2.5 1:4 4kΩ 10000V rms ideal ideal Equivalent Circuits for Magnetically Coupled Coils di1 di2 v1 L1 M dt dt di1 di2 v2 M L2 dt dt Rangkaian Ekivalen model T R1 a + v1 b L1-M i1 M L2-M c i2 + v2 d R2 Rangkaian Ekivalen model R1 L1 L2 M 2 M a i1 + v1 b L1 L2 M 2 L1 M L1 L2 M 2 L2 M c + v2 - d R2 i2 Example j100 500 200 100 j1200 + I1 V1 j 3600 j1600 800 + I2 V2 j 2500 0 3000 V - a. - 6H 1H 3H For the polarity dots shown in this example, M carries a value of +3 H in the T equivalent circuit. L1 M 9 3 6 H L2 M 4 3 1H M 3H At an operating frequency of 400 rad/s, j2400 j400 j1200 V 300 V V 0 700 j 2500 j1200 900 j 2100 V 136 j8 136,24 3,37 V o 300 136 j8 I1 63,25 71,57 o mArms 700 j 2500 136 j8 I2 59,6363,43o mArms 900 j 2100 b). When the polarity dot is moved to the lower terminal of the secondary coil, M carries a value of -3 H in the T equivalent circuit. L1 M 9 3 12 H L2 M 4 3 7 H j4800 j2800 M 3H At an operating frequency of 400 rad/s, -j1200 I1 63,25 71,57 mArms o I 2 59,63 116,57 mArms o V 300 V V 0 700 j 4900 j1200 900 j300 V 8 j 56 56.57 98.130 V rms 300 8 j 56 I1 63.25 71.57 mA rms 700 j 4900 8 j 56 I2 59.63 116.57 0 mA rms 900 j 300 Drill Exercise 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 and a maximum voltage of 245.20 V, and it is operating at 800 rad/s. The transformer parameters are R1 = 100Ω, L1 = 0.5 H, R2 = 40Ω, L2 = 0.125 H, and k = 0.4. Calculate : a). The reflected impedance, b). The primary current, c). The secondary current, and d). The average power delivered to the primary terminals of the transformer. Use the T-equivalent circuit. 15Ω j50Ω + j20Ω 256∠0o V (rms) 80Ω j32Ω V 0 - Calculate : a). The rms magnitude of V0 b). The average power dissipated in the 80 Ω resistor. + - 20 Ω j35Ω 40 j50Ω 15 Ω Ω j45 j80Ω Ω ZL 480∠0 o V (rms) The impedance ZL in the circuit shown is adjusted for maximum average power transfer to ZL. The internal impedance of the sinusoidal voltage source is 20+j35 Ω. What is the maximum average power delivered to ZL? 15mH 20mH 25mH 88Ω 200Ω vg Find the average power delivered to the 200 Ω resistor in the circuit shown if vg= 424 cos 8000t V