## Nodal Analysis of AC Circuit

You will not find the basic theory of the nodal analysis here. We will only cover the step-by-step analyzing the ac circuit using this technique. If you have not learned about the its basic principle, make sure to read Nodal Analysis first.
The following nodal analysis ac circuit examples illustrate this.

Find the i

_{x}in the circuit of Figure.(1) using nodal analysis.Figure 1. Example of nodal ac circuit analysis |

__Solution :__We first convert the circuit to the frequency domain :

Hence, the frequency domain equivalent circuit is as drawn in Figure.(2).

Figure 2. Frequency domain equivalent of the circuit in Figure.(1) |

or

(1.1) |

But

**I**

_{x}=

**V**

_{1}/-

*j*2.5. Substituting this gives

By simplifying, we obtain

(1.2) |

We get the determinants as

The current

**I**

_{x}is given by

Transforming this to the time domain,

## Supernode Analysis of AC Circuit

Next we will analyze an ac circuit containing a supernode in the circuit. Like before, we will not cover the basic principle of supernode used in ac circuit. You need to read Supernode Analysis first in order to understand the following example.

**V**

_{1}and

**V**

_{2}in the circuit of Figure.(3).

Figure 3. Example of supernode ac circuit analysis |

*Solution :*Nodes 1 and 2 form a supernode as drawn in Figure.(4).

Figure 4. Supernode in the circuit |

or

(2.1) |

(2.2) |

From Equation.(2.2),

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