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Consider the network shown in Figure El.3.6 containing a voltage-controlled source producing the controlled current i̟ = gv, where g is a constant with units of conductance, and the control voltage happens to be the terminal voltage in this case. (a) Obtain an expression for Rg = v/i.

Consider the network shown in Figure El.3.6 containing a voltage-controlled source producing the controlled current i̟ = gv, where g is a constant with units of conductance, and the control voltage happens to be the terminal voltage in this case. (a) Obtain an expression for Rg = v/i.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Consider the network shown in Figure E1.3.6 containing a voltage-controlled source producing the controlled current \(i_c = gv\), where \(g\) is a constant with units of conductance, and the control voltage happens to be the terminal voltage in this case. (a) Obtain an expression for \(R_{eq} = v/i\). **Graph/Diagram Explanation:** The problem references a figure, presumably depicting an electrical network with a voltage-controlled current source. The source generates a current \(i_c\) dependent on the voltage \(v\), modulated by a conductance constant \(g\). The expression \(R_{eq}\) is defined as the ratio of voltage \(v\) to current \(i\), likely requiring further analysis or calculation based on elements in the figure not shown in the text.
Transcribed Image Text:Consider the network shown in Figure E1.3.6 containing a voltage-controlled source producing the controlled current \(i_c = gv\), where \(g\) is a constant with units of conductance, and the control voltage happens to be the terminal voltage in this case. (a) Obtain an expression for \(R_{eq} = v/i\). **Graph/Diagram Explanation:** The problem references a figure, presumably depicting an electrical network with a voltage-controlled current source. The source generates a current \(i_c\) dependent on the voltage \(v\), modulated by a conductance constant \(g\). The expression \(R_{eq}\) is defined as the ratio of voltage \(v\) to current \(i\), likely requiring further analysis or calculation based on elements in the figure not shown in the text.
### Figure E1.3.6: Electrical Circuit Diagram This circuit diagram illustrates a simple electrical network containing the following components: 1. **Voltage Source (v)**: Represented on the left with a positive and negative terminal, this component provides a potential difference across the circuit. 2. **Resistor (R)**: Positioned between Node 1 and Node 2, the resistor is marked with the current \( i_R \) flowing through it in the downward direction. The resistor provides resistance to the flow of current. 3. **Controlled Current Source**: Located on the right, it is depicted as a diamond shape with an upward arrow inside, labeled as \( i_c = gv \). This indicates a current source whose magnitude is controlled by the voltage \( v \) across the circuit. 4. **Current Flow (\( i \))**: The current \( i \) is shown flowing from the voltage source toward Node 1, indicating the direction of positive current flow in the circuit. 5. **Nodes**: - **Node 1**: Top connection point where the current \( i_R \) enters the resistor from the voltage source. - **Node 2**: Bottom connection point where current \( i_R \) exits the resistor and connects to the controlled current source. The circuit illustrates the relationship between a voltage source, a resistor, and a controlled current source, showcasing fundamental principles of circuit analysis such as Ohm's Law and Kirchhoff’s laws. The controlled current source is influenced by the voltage \( v \), showing a dependency that can be key in analyzing and designing more complex circuits.
Transcribed Image Text:### Figure E1.3.6: Electrical Circuit Diagram This circuit diagram illustrates a simple electrical network containing the following components: 1. **Voltage Source (v)**: Represented on the left with a positive and negative terminal, this component provides a potential difference across the circuit. 2. **Resistor (R)**: Positioned between Node 1 and Node 2, the resistor is marked with the current \( i_R \) flowing through it in the downward direction. The resistor provides resistance to the flow of current. 3. **Controlled Current Source**: Located on the right, it is depicted as a diamond shape with an upward arrow inside, labeled as \( i_c = gv \). This indicates a current source whose magnitude is controlled by the voltage \( v \) across the circuit. 4. **Current Flow (\( i \))**: The current \( i \) is shown flowing from the voltage source toward Node 1, indicating the direction of positive current flow in the circuit. 5. **Nodes**: - **Node 1**: Top connection point where the current \( i_R \) enters the resistor from the voltage source. - **Node 2**: Bottom connection point where current \( i_R \) exits the resistor and connects to the controlled current source. The circuit illustrates the relationship between a voltage source, a resistor, and a controlled current source, showcasing fundamental principles of circuit analysis such as Ohm's Law and Kirchhoff’s laws. The controlled current source is influenced by the voltage \( v \), showing a dependency that can be key in analyzing and designing more complex circuits.
Expert Solution
Step 1

According to Kirchhoff's current law (KCL), the sum of all the currents entering a node is equal to the sum of all the currents leaving the node. 

In this case, the circuit has only 1 node. 

According to the circuit, 

iR=vR

 

Step 2

Application of KCL at node 1 gives

i+ic=iR=vR=>i=vR-ic=vR-gv=>i=v1R-g--->(1)

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