thevenin - Thevenin Equivalent Circuits Introduction In...

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Thevenin Equivalent Circuits Introduction In each of these problems, we are shown a circuit and its Thevenin or Norton equivalent circuit. The Thevenin and Norton equivalent circuits are described using three parameters: V oc , the open circuit voltage of the circuit, I sc , the short circuit of the circuit and R th , the Thevenin resistance of the circuit. Each problem, asks us to determine the value of asked to determine the value of V oc , I sc or R th . Thevenin equivalent circuits are discussed in Section 5.5 of Introduction to Electric Circuits by R.C. Dorf and J.A Svoboda. Norton equivalent circuits are discussed in Section 5.6. Worked Examples Example 1: The circuit shown in Figure 1b is the Thevenin equivalent circuit of the circuit shown in Figure 1a. Find the value of the open circuit voltage, V oc and Thevenin resistance, R th . Figure 1 The circuit considered in Example 1. Solution: The circuit from Figure 1a can be reduced to its Thevenin equivalent circuit in four steps shown in Figure 2a, b, c and d. A source transformation transforms the series voltage source and 20 resistor in Figure 1a into the parallel current source and 20 resistor in Figure 2a. The current source current is calculated from the voltage source voltage and resistance as 20 V 1 A 20 = . After the source transformation, the 20 resistor is parallel to the 80 resistor. Replacing these parallel resistors with the equivalent 16 resistor produces the circuit shown in Figure 2b. 2
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A second source transformation transforms the parallel current source and 16 resistor in Figure 2b into the series voltage source and 16 resistor in Figure 2c. The voltage source voltage is calculated from the current source current and resistance as ( )( ) 1 A 16 16 V Ω = . After the source transformation, the two16 resistors are in series. Replacing these series resistors with the equivalent 32 resistor produces the circuit shown in Figure 2d. Comparing Figure 2d to Figure 1b shows that the Thevenin resistance is R th = 32 and the open circuit voltage, V oc = -16 V. ( a ) ( b ) ( c ) ( d ) Figure 2 The circuit from Figure 1a can be reduced to its Thevenin equivalent circuit in four steps shown here as ( a ), ( b ), ( c ), and ( d ). 3
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Example 2: The circuit shown in Figure 3b is the Thevenin equivalent circuit of the circuit shown in Figure 1a. Find the value of the open circuit voltage, V oc and Thevenin resistance, R th . Figure 3 The circuit considered in Example 2. Solution: The circuit from Figure 3a can be reduced to its Thevenin equivalent circuit in five steps shown in Figure 4a, b, c, d and e. A source transformation transforms the parallel current source and 3 resistor in Figure 3a into the series voltage source and 3 resistor in Figure 4a. The voltage source voltage is calculated from the current source current and resistance as ( )( ) 2 A 3 6 V Ω = . After the source transformation, the 3 and 6 resistors are in series. Also, the 6V and 3 V voltage sources are in series. Replacing the series resistors with the equivalent 9
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