Determine currents , , and in the circuit of Fig. 13.89.

For the three coupled coils in Fig. 13.72, calculate the total inductance.

Using Fig. 13.73, design a problem to help other students better understand mutual inductance.

Two coils connected in series-aiding fashion have a total inductance of 500 mH. When connected in a series-opposing configuration, the coils have a total inductance of 300 mH. If the inductance of one coil ( ) is three times the other, find and M. What is the coupling coefficient?

(a) For the coupled coils in Fig. 13.74(a), show that (b) For the coupled coils in Fig. 13.74(b), show that Leq L1L2  M2 L1 L2  2M

Two coils are mutually coupled, with and . Calculate the maximum possible equivalent inductance if: (a) the two coils are connected in series (b) the coils are connected in parallel

The coils in Fig. 13.75 have and coupling coefficient Find and given that 4 sinvt, v 2000 rad/s. v1(t) 20 cosvt and i2(t)

For the circuit in Fig. 13.76, find .

Find v(t) for the circuit in Fig. 13.77.

Find in the network shown in Fig. 13.78.

Find in the circuit of Fig. 13.79.

Use mesh analysis to find in Fig. 13.80, where is 4 cos(600t) A and vs 110 cos(600t 30) i

Determine the equivalent in the circuit of Fig. 13.81.

For the circuit in Fig. 13.82, determine the impedance seen by the source.

Obtain the Thevenin equivalent circuit for the circuit in Fig. 13.83 at terminals a-b.

Find the Norton equivalent for the circuit in Fig. 13.84 at terminals a-b.

Obtain the Norton equivalent at terminals a-b of the circuit in Fig. 13.85.

In the circuit of Fig. 13.86, is a 15-mH inductor having an impedance of Determine when k 0.6.

Find the Thevenin equivalent to the left of the load Z in the circuit of Fig. 13.87.

Determine an equivalent T-section that can be used to replace the transformer in Fig. 13.88.

Determine currents , , and in the circuit of Fig. 13.89. Find the energy stored in the coupled coils at Take t 2 ms. 1,000 rad/s. I

Using Fig. 13.90, design a problem to help other students better understand energy in a coupled circuit.

Find current in the circuit of Fig. 13.91.

If and in the circuit of Fig. 13.92, find and Calculate the energy stored in the coupled coils at ms.

In the circuit of Fig. 13.93, (a) find the coupling coefficient, (b) calculate , (c) determine the energy stored in the coupled inductors at t 2 s.

For the network in Fig. 13.94, find and Io Z .

Find in the circuit of Fig. 13.95. Switch the dot on the winding on the right and calculate again.

Find the average power delivered to the resistor in the circuit of Fig. 13.96.

In the circuit of Fig. 13.97, find the value of X that will give maximum power transfer to the 20- load.

In the circuit of Fig. 13.98, find the value of the coupling coefficient that will make the resistor dissipate 320 W. For this value of k, find the energy stored in the coupled coils at t 1.5 s.

(a) Find the input impedance of the circuit in Fig. 13.99 using the concept of reflected impedance. (b) Obtain the input impedance by replacing the linear transformer by its T equivalent.

Using Fig. 13.100, design a problem to help other students better understand linear transformers and how to find T-equivalent and -equivalent circuits.

Two linear transformers are cascaded as shown in Fig. 13.101. Show that Zin 2 R(La 2 LaLb  M2 a) j3 (L2 aLb LaL2 b  LaM2 b  LbM2 a) 2 (LaLb L2 b  M2 b)  jR(La Lb) ale8057

Determine the input impedance of the air-core transformer circuit of Fig. 13.102.

Using Fig. 13.103, design a problem to help other students better understand how to find the input impedance of circuits with transformers.

Find currents , , and in the circuit of Fig. 13.104.

As done in Fig. 13.32, obtain the relationships between terminal voltages and currents for each of the ideal transformers in Fig. 13.105.

A 480/2,400-V rms step-up ideal transformer delivers 50 kW to a resistive load. Calculate: (a) the turns ratio (b) the primary current (c) the secondary current

Design a problem to help other students better understand ideal transformers.

A 1,200/240-V rms transformer has impedance on the high-voltage side. If the transformer is connected to a load on the low-voltage side, determine the primary and secondary currents when the transformer is connected to 1200 V rms.

The primary of an ideal transformer with a turns ratio of 5 is connected to a voltage source with Thevenin parameters and Determine the average power delivered to a load connected across the secondary winding.

Determine and in the circuit of Fig. 13.106.

For the circuit in Fig. 13.107, determine the power absorbed by the resistor. Assume the 80 V is an rms value.

Obtain and in the ideal transformer circuit of Fig. 13.108.

In the ideal transformer circuit of Fig. 13.109, find and .

For the circuit shown in Fig. 13.110, find the value of the average power absorbed by the resistor.

(a) Find and in the circuit of Fig. 13.111 below. (b) Switch the dot on one of the windings. Find and again.

Find v(t) for the circuit in Fig. 13.112.

Using Fig. 13.113, design a problem to help other students better understand how ideal transformers work.

Find current in the ideal transformer circuit shown in Fig. 13.114.

Calculate the input impedance for the network in Fig. 13.115.

Use the concept of reflected impedance to find the input impedance and current in Fig. 13.116.

For the circuit in Fig. 13.117, determine the turns ratio n that will cause maximum average power transfer to the load. Calculate that maximum average power.

Refer to the network in Fig. 13.118. (a) Find n for maximum power supplied to the load. (b) Determine the power in the load if n 10.

A transformer is used to match an amplifier with an load as shown in Fig. 13.119. The Thevenin equivalent of the amplifier is: . (a) Find the required turns ratio for maximum energy power transfer. (b) Determine the primary and secondary currents. (c) Calculate the primary and secondary voltages.

For the circuit in Fig. 13.120, calculate the equivalent resistance.

Find the power absorbed by the resistor in the ideal transformer circuit of Fig. 13.121.

For the ideal transformer circuit of Fig. 13.122 below, find: (a) and , (b) , , and , (c) the complex power supplied by the source.

Determine the average power absorbed by each resistor in the circuit of Fig. 13.123.

In the circuit of Fig. 13.124, let Find the average power delivered to each resistor.

Refer to the circuit in Fig. 13.125 on the following page. (a) Find currents , , and . (b) Find the power dissipated in the resistor.

For the circuit in Fig. 13.126, find and Vo I .

For the network in Fig. 13.127, find: (a) the complex power supplied by the source, (b) the average power delivered to the resistor

Find the mesh currents in the circuit of Fig. 13.128

For the circuit in Fig. 13.129, find the turns ratio so that the maximum power is delivered to the resistor

Calculate the average power dissipated by the resistor in Fig. 13.130.

Design a problem to help other students better understand how the ideal autotransformer works.

An autotransformer with a 40 percent tap is supplied by a 400-V, 60-Hz source and is used for stepdown operation. A 5-kVA load operating at unity power factor is connected to the secondary terminals. Find: (a) the secondary voltage (b) the secondary current (c) the primary current

In the ideal autotransformer of Fig. 13.131, calculate and Find the average power delivered to the load.

In the circuit of Fig. 13.132, is adjusted until maximum average power is delivered to Find and the maximum average power transferred to it. Take turns and turns.

In the ideal transformer circuit shown in Fig. 13.133, determine the average power delivered to the load.

In the autotransformer circuit in Fig. 13.134, show that Zin a1 N1 N2 b 2 ZL

In order to meet an emergency, three single-phase transformers with 12,470/7,200 V rms are connected in -Y to form a three-phase transformer which is fed by a 12,470-V transmission line. If the transformer supplies 60 MVA to a load, find: (a) the turns ratio for each transformer, (b) the currents in the primary and secondary windings of the transformer, (c) the incoming and outgoing transmission line currents.

Figure 13.135 on the following page shows a threephase transformer that supplies a Y-connected load. (a) Identify the transformer connection. (b) Calculate currents and . (c) Find the average power absorbed by the load.

Consider the three-phase transformer shown in Fig. 13.136. The primary is fed by a three-phase source with line voltage of 2.4 kV rms, while the secondary supplies a three-phase 120-kW balanced load at pf of 0.8. Determine: (a) the type of transformer connections, (b) the values of and , (c) the values of and , (d) the kVA rating of each phase of the transformer.

A balanced three-phase transformer bank with the -Y connection depicted in Fig. 13.137 is used to step down line voltages from 4,500 V rms to 900 V rms. If the transformer feeds a 120-kVA load, find: (a) the turns ratio for the transformer, (b) the line currents at the primary and secondary sides.

Using Fig. 13.138, design a problem to help other students better understand a Y- , three-phase transformer and how they work.

The three-phase system of a town distributes power with a line voltage of 13.2 kV. A pole transformer connected to single wire and ground steps down the high-voltage wire to 120 V rms and serves a house as shown in Fig. 13.139. (a) Calculate the turns ratio of the pole transformer to get 120 V. (b) Determine how much current a 100-W lamp connected to the 120-V hot line draws from the high-voltage line.

Use PSpice or MultiSim to determine the mesh currents in the circuit of Fig. 13.140. Take 1 rad/s. Use when solving this problem. k

Use PSpice or MultiSim to find and in the circuit of Fig. 13.141.

Rework Prob. 13.22 using PSpice or Multisim.

Use PSpice or MultiSim to find , , and in the circuit of Fig. 13.142.

Use PSpice or MultiSim to find , , and in the circuit of Fig. 13.143.

Find and in the circuit of Fig. 13.144 using PSpice or MultiSim.

Determine , and in the ideal transformer circuit of Fig. 13.145 using PSpice or MultiSim.

A stereo amplifier circuit with an output impedance of is to be matched to a speaker with an input impedance of by a transformer whose primary side has 3,000 turns. Calculate the number of turns required on the secondary side.

A transformer having 2,400 turns on the primary and 48 turns on the secondary is used as an impedancematching device. What is the reflected value of a load connected to the secondary?

A radio receiver has an input resistance of . When it is connected directly to an antenna system with a characteristic impedance of , an impedance mismatch occurs. By inserting an impedance-matching transformer ahead of the receiver, maximum power can be realized. Calculate the required turns ratio.

A step-down power transformer with a turns ratio of supplies 12.6 V rms to a resistive load. If the primary current is 2.5 A rms, how much power is delivered to the load?

A 240/120-V rms power transformer is rated at 10 kVA. Determine the turns ratio, the primary current, and the secondary current.

A 4-kVA, 2,400/240-V rms transformer has 250 turns on the primary side. Calculate: (a) the turns ratio, (b) the number of turns on the secondary side, (c) the primary and secondary currents.

A 25,000/240-V rms distribution transformer has a primary current rating of 75 A. (a) Find the transformer kVA rating. (b) Calculate the secondary current.

A 4,800-V rms transmission line feeds a distribution transformer with 1,200 turns on the primary and 28 turns on the secondary. When a load is connected across the secondary, find: (a) the secondary voltage, (b) the primary and secondary currents, (c) the power supplied to the load.

A four-winding transformer (Fig. 13.146) is often used in equipment (e.g., PCs, VCRs) that may be operated from either 110 V or 220 V. This makes the equipment suitable for both domestic and foreign use. Show which connections are necessary to provide: (a) an output of 14 V with an input of 110 V, (b) an output of 50 V with an input of 220 V.

A 440/110-V ideal transformer can be connected to become a 550/440-V ideal autotransformer. There are four possible connections, two of which are wrong. Find the output voltage of: (a) a wrong connection, (b) the right connection.

Ten bulbs in parallel are supplied by a 7,200/120-V transformer as shown in Fig. 13.147, where the bulbs are modeled by the resistors. Find: (a) the turns ratio n, (b) the current through the primary winding.

Some modern power transmission systems now have major high-voltage DC transmission segments. There are a lot of good reasons for doing this but we will not go into them here. To go from the AC to DC, power electronics are used. We start with three-phase AC and then rectify it (using a full-wave rectifier). It was found that using a delta to wye and delta combination connected secondary would give us a much smaller ripple after the full-wave rectifier. How is this accomplished? Remember that these are real devices and are wound on common cores. Hint: Use Figs. 13.47 and 13.49, and the fact that each coil of the wye connected secondary and each coil of the delta connected secondary are wound around the same core of each coil of the delta connected primary so the voltage of each of the corresponding coils are in phase. When the output leads of both secondaries are connected through fullwave rectifiers with the same load, you will see that the ripple is now greatly reduced. Please consult the instructor for more help if necessary