Find the load impedance as seen from the primary side of the transformer if: a = 3, lp= 5A, and Vg = 140V N₂ Ns Zin = +₁₁ ell ell IL units + ZL VL
Find the load impedance as seen from the primary side of the transformer if: a = 3, lp= 5A, and Vg = 140V N₂ Ns Zin = +₁₁ ell ell IL units + ZL VL
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Three-Phase Transformers
Three-segment transformers are a type of transformer used to transform voltages of electrical systems into three ranges. Two type transformers are shell-type transformer and core type transformer. In brief, it could be described because of the exquisite kinds of configurations.
Transformer
Ever since electricity has been created, people have started using it in its entirety. We see many types of Transformers in the neighborhoods. Some are smaller in size and some are very large. They are used according to their requirements. Many of us have seen the electrical transformer but they do not know what work they are engaged in.
Question
![**Transformer Circuit Analysis:**
The given image illustrates a transformer circuit with labeled components for analysis. Below is a breakdown of the key elements and specifications provided:
1. **Components and Labels:**
- A source voltage, \( V_g \), which is 140V.
- A primary winding with a current, \( I_p = 5A \).
- A secondary winding connected to a load impedance, \( Z_L \).
- The turns ratio, \( a = 3 \), between the primary and secondary windings.
- Symbols for voltages, \( V_g \) and \( V_L \), represent the voltage on the primary and secondary sides respectively.
- Currents, \( I_p \) and \( I_L \), indicate current flow through the primary and secondary coils respectively.
2. **Transformer Portrayal:**
- **Primary Side:** Denoted by the subscript 'p', it connects to the source voltage \( V_g \) and carries current \( I_p \).
- **Secondary Side:** Denoted by the subscript 's', it forms a closed loop with the load impedance \( Z_L \), carrying current \( I_L \).
- The depiction shows directionality for current and voltage, aiding in circuit analysis and understanding the power flow through the device.
3. **Objective:**
- The primary aim is to find the load impedance as it appears from the primary side of the transformer, denoted as \( Z_{in} \).
4. **Equations and Analysis:**
- The relation between primary and secondary currents and voltages is dictated by the transformer's turns ratio (\( a \)):
\[
a = \frac{N_p}{N_s} = \frac{V_p}{V_s} = \frac{I_s}{I_p}
\]
- The load impedance as seen from the primary side, \( Z_{in} \), is calculated using the formula:
\[
Z_{in} = \left(\frac{V_g}{I_p}\right) \text{ units}
\]
**Note:** To solve for \( Z_{in} \), use the relevant transformer equations considering the turns ratio and given values. The answer will define the impedance viewable from the primary side, crucial for determining the performance and efficiency of the transformer in the circuit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F946d2131-1df4-4d93-acc7-a27f80ccabfd%2F2d5bf14d-891d-4814-837f-eafa5eecd39f%2F84s6o3l8_processed.png&w=3840&q=75)
Transcribed Image Text:**Transformer Circuit Analysis:**
The given image illustrates a transformer circuit with labeled components for analysis. Below is a breakdown of the key elements and specifications provided:
1. **Components and Labels:**
- A source voltage, \( V_g \), which is 140V.
- A primary winding with a current, \( I_p = 5A \).
- A secondary winding connected to a load impedance, \( Z_L \).
- The turns ratio, \( a = 3 \), between the primary and secondary windings.
- Symbols for voltages, \( V_g \) and \( V_L \), represent the voltage on the primary and secondary sides respectively.
- Currents, \( I_p \) and \( I_L \), indicate current flow through the primary and secondary coils respectively.
2. **Transformer Portrayal:**
- **Primary Side:** Denoted by the subscript 'p', it connects to the source voltage \( V_g \) and carries current \( I_p \).
- **Secondary Side:** Denoted by the subscript 's', it forms a closed loop with the load impedance \( Z_L \), carrying current \( I_L \).
- The depiction shows directionality for current and voltage, aiding in circuit analysis and understanding the power flow through the device.
3. **Objective:**
- The primary aim is to find the load impedance as it appears from the primary side of the transformer, denoted as \( Z_{in} \).
4. **Equations and Analysis:**
- The relation between primary and secondary currents and voltages is dictated by the transformer's turns ratio (\( a \)):
\[
a = \frac{N_p}{N_s} = \frac{V_p}{V_s} = \frac{I_s}{I_p}
\]
- The load impedance as seen from the primary side, \( Z_{in} \), is calculated using the formula:
\[
Z_{in} = \left(\frac{V_g}{I_p}\right) \text{ units}
\]
**Note:** To solve for \( Z_{in} \), use the relevant transformer equations considering the turns ratio and given values. The answer will define the impedance viewable from the primary side, crucial for determining the performance and efficiency of the transformer in the circuit.
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