Voltage and Current Division

Voltage and Current Division - Voltage and Current Division...

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Voltage and Current Division Introduction The circuits in this problem set consist of a single voltage or current source, some resistors and a voltmeter or ammeter. The input to each circuit is the voltage of the voltage source or the current of the current source. The output of each circuit is either the voltage measured by the voltmeter or the current measured by the ammeter. All of the inputs have constant values. Consequently, the outputs also have constant values. The output of each circuit is proportional to the input to that circuit. Each circuit includes resistors that are connected either in series or in parallel. The problems in this problem set can be solved using the principles of voltage division, current division or equivalent resistance. Series resistors and voltage division are discussed in Section 3.4 of Introduction to Electric Circuits by R.C. Dorf and J.A Svoboda. Parallel resistors and current division are discussed in Section 3.4. These ideas are summarized in Table 3.12-1 of Introduction to Electric Circuits . Worked Examples Example 1: Consider the voltage divider circuit shown in Figure 1. Find the value of the resistance R . Determine the power supplied by the voltage source. Figure 1 The circuit considered in Example 1. Solution: The voltmeter measures the voltage across the 4 resistor to be –6 V. (The color coded probes of the voltmeter indicate the reference direction of the voltage measured by the voltmeter.) Figure 2a shows the circuit after the replacing the voltmeter by the equivalent open circuit and adding a label to show the voltage measured by the meter. Figure 2b shows the voltage divider circuit again, this time with the voltage across the 4 resistor labeled as v a . The voltage division equation gives 1
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4 15 4 a v R = + (1) The reference direction for v a
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