Consider the seven-element circuit depicted in Fig. 3.99. (a) How many nodes, loops, and branches does it contain? (b) Calculate the current flowing through each resistor. (c) Determine the voltage across the current source, assuming the top terminal is the positive reference terminal.
■ FIGURE 3.99
(a)
Find the number of nodes, number of loops and number of branches in the circuit.
Answer to Problem 63E
Number of nodes in the circuit is
Explanation of Solution
The circuit diagram is redrawn as shown in Figure 1.
Refer to the redrawn Figure 1.
A point where two or more branches have common connection is known as node.
In Figure 1 two branches are connected at point
Each electrical element or device present in the circuit is known as branch.
There is
The circuit diagram is redrawn as shown in Figure 2,
Refer to the redrawn Figure 2,
If starting and ending node is same for a path then it is known as closed path or loop.
Conclusion:
Thus, the number of nodes in the circuit is
(b)
Find the value of current through each resistor.
Answer to Problem 63E
The value of current through
Explanation of Solution
Formula used:
The expression for parallel combination of resistance is as follows.
Here,
Calculation:
The circuit diagram is redrawn as shown in Figure 3.
Refer to the redrawn Figure 3.
The expression for current
Here,
The expression for current
Here,
Refer to the redrawn Figure 1.
The expression for current
Here,
The expression for current
Here,
Refer to the redrawn Figure 1.
As
Rearrange for
Refer to the redrawn Figure 3.
As current source direction is downward means change sign of current means value of current is
Substitute
As resistor
So value of current through resistor
Substitute
So, the value of current through resistor
Refer to the redrawn Figure 1.
Substitute
So, the value of current through resistor
Substitute
So, the value of current through resistor
As resistor
Conclusion:
Thus, the value of current through
(c)
Find value of voltage across current source.
Answer to Problem 63E
The voltage across current source is
Explanation of Solution
Formula used:
The expression for voltage is as follows.
Here,
Calculation:
Refer to the redrawn Figure 3.
The expression for voltage
Here,
Refer to the redrawn Figure 3.
Substitute
So value of voltage
Substitute
So value of voltage
Substitute
Conclusion:
Thus, the voltage across current source is
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Chapter 3 Solutions
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