CLARKSON ES 250 - EXAMPLES (6 pages)

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EXAMPLES

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EXAMPLES

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6
School:
Clarkson University
Course:
Es 250 - ELECTRICAL SCIENCE
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Example The circuit shown in a has been divided into two parts In b the right hand part has been replaced with an equivalent circuit The left hand part of the circuit has not been changed Determine the value of the current i2 Solution 1 Determine the value of the resistance R in b that makes the circuit in b equivalent to the circuit in a 10 40 20 R 12 10 40 2 Find the current i and the voltage v shown in b R is in parallel with the 80 resistor The equivalent resistance R 80 is in series with the 16 resistor Using voltage division gives 20 80 R 80 16 v 20 80 8 8 4 V 16 R 80 16 20 80 16 16 20 80 Using Ohm s law 4 i 0 2 A 20 Because of the equivalence the current i and the voltage v shown in a are equal to the current i and the voltage v shown in b 3 Find the current i2 shown from i using current division i2 10 10 i 0 2 0 04 A 40 mA 10 40 50 How can we check our calculations Let s apply KVL to the loop shown below We get 12 i 40 i 2 v 0 Notice that this equation involves all three of the values that we calculated If our values satisfy this equation it s likely that they are correct Substituting the calculated values gives 12 0 2 40 0 04 4 2 4 1 6 4 0 The calculated values do satisfy the KVL equation and it s likely that they are correct Suppose we aren t satisfied and want to check further Apply KCL at the top node of the 80 resistor to get 8 v v i 16 80 Substituting the calculated values into this equation gives 8 4 4 0 2 0 25 0 05 0 2 16 80 The calculated values do satisfy this KCL equation We can be confident that they are correct Example The circuit shown in a has been divided into three parts In b the rightmost part has been replaced with an equivalent circuit The rest of the circuit has not been changed The circuit is simplified further in c Now the middle and rightmost parts have been replaced by a single equivalent resistance The leftmost part of the circuit is still unchanged Solution 1 Determine the value of the resistance R1 in b that makes the circuit in b

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