- Network Theory Tutorial
- Network Theory - Home
- Network Theory - Overview
- Example Problems
- Network Theory - Active Elements
- Network Theory - Passive Elements
- Network Theory - Kirchhoff’s Laws
- Electrical Quantity Division Principles
- Network Theory - Nodal Analysis
- Network Theory - Mesh Analysis
- Network Theory - Equivalent Circuits
- Equivalent Circuits Example Problem
- Delta to Star Conversion
- Star to Delta Conversion
- Network Theory - Network Topology
- Network Topology Matrices
- Superposition Theorem
- Thevenin’s Theorem
- Network Theory - Norton’s Theorem
- Maximum Power Transfer Theorem
- Response of DC Circuits
- Response of AC Circuits
- Network Theory - Series Resonance
- Parallel Resonance
- Network Theory - Coupled Circuits
- Two-Port Networks
- Two-Port Parameter Conversions
- Network Theory - Filters

- Network Theory Useful Resources
- Network Theory - Quick Guide
- Network Theory - Useful Resources
- Network Theory - Discussion

- Selected Reading
- UPSC IAS Exams Notes
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# Network Theory - Example Problems

We discussed the types of network elements in the previous chapter. Now, let us identify the **nature of network elements** from the V-I characteristics given in the following examples.

## Example 1

The **V-I characteristics** of a network element is shown below.

**Step 1** − Verifying the network element as **linear** or **non-linear**.

From the above figure, the V-I characteristics of a network element is a straight line passing through the origin. Hence, it is a **Linear element**.

**Step 2** − Verifying the network element as **active** or **passive**.

The given V-I characteristics of a network element lies in the first and third quadrants.

In the

**first quadrant**, the values of both voltage (V) and current (I) are positive. So, the ratios of voltage (V) and current (I) gives positive impedance values.Similarly, in the

**third quadrant**, the values of both voltage (V) and current (I) have negative values. So, the ratios of voltage (V) and current (I) produce positive impedance values.

Since, the given V-I characteristics offer positive impedance values, the network element is a **Passive element**.

**Step 3** − Verifying the network element as **bilateral** or **unilateral**.

For every point (I, V) on the characteristics, there exists a corresponding point (-I, -V) on the given characteristics. Hence, the network element is a **Bilateral element**.

Therefore, the given V-I characteristics show that the network element is a **Linear, Passive**, and **Bilateral element**.

## Example 2

The **V-I characteristics** of a network element is shown below.

**Step 1** − Verifying the network element as **linear** or **non-linear**.

From the above figure, the V-I characteristics of a network element is a straight line only between the points (-3A, -3V) and (5A, 5V). Beyond these points, the V-I characteristics are not following the linear relation. Hence, it is a **Non-linear element**.

**Step 2** − Verifying the network element as **active** or **passive**.

The given V-I characteristics of a network element lies in the first and third quadrants. In these two quadrants, the ratios of voltage (V) and current (I) produce positive impedance values. Hence, the network element is a **Passive element**.

**Step 3** − Verifying the network element as **bilateral or unilateral**.

Consider the point (5A, 5V) on the characteristics. The corresponding point (-5A, -3V) exists on the given characteristics instead of (-5A, -5V). Hence, the network element is a **Unilateral element**.

Therefore, the given V-I characteristics show that the network element is a **Non-linear, Passive**, and **Unilateral element**.