Solve the circuit using nodal analysis and determine the power of 
.
Solution
I. Identify all nodes in the circuit. The circuit contains 3 nodes, as illustrated below.
Author: Yaz
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Problem 1-11: Solving a Circuit with Three Nodes by the Nodal Analysis
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Problem 1-10: Solving by Nodal Analysis – Circuit with Four Nodes
Let’s use nodal analysis to solve this circuit and determine
.
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Solution
I. Identify all nodes in the circuit. There are four nodes in the circuit, as indicated below -
Problem 1-9: Power of a Current Source
Find the power of
using circuit reduction methods.
Solution
and 
are parallel. 
and 
are also parallel. Therefore:
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Problem 1-8: Nodal Analysis – Power of Current Source
Solve the circuit using nodal analysis and find the power of
.
Solution
a) Choose a reference node, label the voltages:
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Problem 1-7: Circuit Reduction – Current Divider
Find
(Hint: use circuit reduction).
All resistors are
and 
Solution
Let’s redraw the circuit:
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Problem 1-6: Single Node-Pair Analysis
Find
using single node-pair analysis (do not reduce the circuit).
and 
.
Solution
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a) Redraw the circuit if necessary. Mark the voltage across nodes: -
Problem 1-5: Single Loop Analysis
Find
using single loop analysis (do not reduce the circuit).
and .
Solution
a) Choose loop current:
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Problem 2-11: Differentiating by Chain Rule
Differentiate
by using the chain rule. -
Problem 2-9: Differentiating Polynomial and Rational Functions
Differentiate
a)
b)
c)
d)
Solution
The following rules can be used:
I)
II)
III)
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