Equivalent Circuits

Equivalent Circuits - Equivalent Circuits Introduction The...

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Equivalent Circuits Introduction The circuits in this set of problems consist of a voltage or current source and several resistors. The resistors are connected together to form a “resistor sub-circuit”. These circuits can be simplified by repeatedly replacing series or parallel resistors by an equivalent resistor. Eventually, the resistor sub-circuit is reduced to a single equivalent resistor. In each problem we are asked to determine the values of three currents or voltages. These currents or voltages are identified by the subscripts a, b and c. The computer will guide us to a solution in three steps: 1. Reduce the resistor sub-circuit to a single resistor. 2. Analyze the reduced circuit, using Ohm’s law, to find the resistor current and voltage. Then determine the values of the source current and voltage in the reduced circuit. The values of the source current and voltage in the original circuit are the same as the values of the source current and voltage in the reduced circuit. 3. Complete the analysis of the original circuit using voltage or current division. Series resistors are discussed in Section 3.4 of Introduction to Electric Circuits by R.C. Dorf and J.A Svoboda. Parallel resistors are discussed in Section 3.5. Circuit analysis using equivalent resistances is described in Section 3.7. Worked Examples Example 1: Consider the circuit shown in Figure 1. Find the values of the voltage v c and the current i b . Figure 1 The circuit considered in Example 1. 1
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Solution: The terminals in Figure 1 divide the circuit into two parts, the part to the left of the terminals and the part to the right of the terminals. The part to the right of the terminals consists of three resistors. The 10 resistor is connected in parallel with the 40 resistor and that parallel combination is connected in series with the 4 resistor. These three resistors can be replaced by a single equivalent resistor as shown in Figure 2a. The resistance of the equivalent resistor is given by ( )( ) 10 40 44 8 10 40 eq R 1 2 = += + = + The current in the equivalent resistance is determined using Ohm’s law to be 24 2 A 12 a i == The values of the equivalent resistance and the current i a are labeled in Figure 2b.
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Equivalent Circuits - Equivalent Circuits Introduction The...

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