Question:
In the given circuit, the current \(I_x\) (in mA) is \(\_\_\_\_\).
\begin{center}
\includegraphics[width=8cm]{31.png}
\end{center}
In the given circuit, the current \(I_x\) (in mA) is \(\_\_\_\_\).
\begin{center}
\includegraphics[width=8cm]{31.png}
\end{center}
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For circuits with dependent sources, systematically apply KCL at critical nodes and use current division rules to find unknown currents.
Updated On: Jan 31, 2025
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Solution and Explanation
Step 1: Apply current division principles.
The circuit consists of a 5 mA current source, a dependent current source \(1000 I_0\), and resistors. Use Kirchhoff's Current Law (KCL) to analyze the node with \(I_x\). Step 2: Define the known currents.
Given \(I_0 = 2 \, {mA}\), the dependent source generates a current of: \[ 1000 I_0 = 1000 \times 2 \, {mA} = 2 \, {A}. \] Step 3: Determine \(I_x\).
The current \(I_x\) flows through the 1 k\(\Omega\) resistor. Based on current division and balancing the node currents, we find: \[ I_x = 2 \, {mA}. \] Final Answer: \[\boxed{{2}}\]
The circuit consists of a 5 mA current source, a dependent current source \(1000 I_0\), and resistors. Use Kirchhoff's Current Law (KCL) to analyze the node with \(I_x\). Step 2: Define the known currents.
Given \(I_0 = 2 \, {mA}\), the dependent source generates a current of: \[ 1000 I_0 = 1000 \times 2 \, {mA} = 2 \, {A}. \] Step 3: Determine \(I_x\).
The current \(I_x\) flows through the 1 k\(\Omega\) resistor. Based on current division and balancing the node currents, we find: \[ I_x = 2 \, {mA}. \] Final Answer: \[\boxed{{2}}\]
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