3.4 The Single-Loop Circuit Single-loop circuits

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1 The Single-Loop Circuit Single-loop circuits Elements are connected in series All elements carry the same current We shall determine The current through each element The voltage across each element The power absorbed by each element

2 The Single-Loop Circuit Single-loop circuits Elements are connected in series All elements carry the same current We shall determine The current through each element The voltage across each element The power absorbed by each element We apply the following steps 1) Assign a reference direction for the unknown current 2) Assign voltage references to the elements 3)Apply KVL to the closed loop path KVL 4)Use Ohm's law where needed to get an equation in i 5)Solve for i

3 27 Find i and p for all elements in the circuit Ans: KVL 1) Assign a reference direction for the unknown current 2)Assign voltage references to the elements (note that v A =-v 2 ) 3)Apply KVL to the closed loop path 4)Use Ohms law where needed to get an equation in i 5)Solve for i

4 28 Find i and p for all elements in the circuit Ans: KVL Computing the power absorbed by each element The total power absorbed by all elements

5 The Single-Node-Pair Circuit Single-node-pair circuits Elements are connected in parallel All elements have a common voltage We shall determine The current through each element The voltage across each element The power absorbed by each element

6 The Single-Node-Pair Circuit Single-node-pair circuits Elements are connected in parallel All elements have a common voltage We shall determine The current through each element The voltage across each element The power absorbed by each element We apply the following steps 1) Define the voltage v and arbitrary select its polarity 2) Use passive sign convention to determine the currents directions 3)Apply KCL at the node 4)Use Ohm's law where needed to get an equation in v 5)Solve for v

7 31 Find v and p supplied by the independent source Ans: 1) Assign an arbitrary sign for the unknown voltage 2)passive sign convention to find the currents directions (note that ix=-i 2 ) 3)Apply KCL to the nodes 4)Use Ohm's law where needed to get an equation in v 5)Solve for v

8 32 HW: Find i 1, i 2, i 3, and i 4

9 Series and Parallel Connected Sources Series-connected voltage sources can be replaced by a single source Parallel current sources can be replaced by a single source

10 Resistors Series and Parallel Series connection KVL Parallel connection

11 35 Find the voltage and the power of the independent source 1)Apply KCL at the top node 2)Use Ohm's law for (i 1 =v x /6) and (v x =3i 3 ) 3) Solve i 3 and v x

12 Voltage and Current Division Voltage divider: is a passive linear circuit that produces an output voltage (v out ) that is a fraction of its input voltage (v in ) Easily solved with KCL, KVL, & equivalent resistances Then, Generally, assume we have The voltage v N can be given as Easy to find the other voltages, too

13 37

14 38 Current divider: is a simple linear circuit that produces an output current (i out ) that is a fraction of its input current (i in ) Easily solved with Since For n=2, we have The circuit divider reduces to

15 39 Use resistance combination methods and current division to find i 1 and i 2 and v x Ans: We note i 1 goes to the following equivalent resistor Use current divider, we have

16 40 We note i 2 goes to the following equivalent resistor Use current divider, we have HW: Solve v x

17 41 We note i 2 goes to the following equivalent resistor Use current divider, we have HW: Solve v x Homework Assignment 2 P3.6, P3.7, P3.13, P3.15, P3.16, P3.19, P3.20, P3.21, P3.30, P3.31, P3.35, P3.39, P3.73, P3.75 and P3.82

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