Find the marked current and voltage in the following figure 1.

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**Problem:**

Find the marked current \( i \) and voltage \( V_x \) in the following circuit diagram.

**Diagram Description:**

The circuit consists of a network of resistors and a voltage source. Here’s a detailed breakdown of the circuit:

1. **Voltage Source:**
   - A 10V voltage source is connected on the left side of the circuit.

2. **Resistors:**
   - Multiple resistors are connected in the circuit with the following resistances:
     - Two 5Ω resistors
     - Two 20Ω resistors
     - Six 10Ω resistors

3. **Connections:**
   - The top path from left to right includes two consecutive 10Ω resistors.
   - Below the top path, in a triangular configuration, there is a 5Ω resistor in series from the + terminal of the voltage source leading to a 20Ω resistor, followed by another 5Ω resistor.
   - The middle horizontal line consists of two 10Ω resistors.
   - Below this line, another set of configurations includes a 5Ω, a 10Ω, and another set with 20Ω connected vertically on the right side.
   - Bottom line includes two 10Ω resistors.

4. **Current and Voltage Markings:**
   - The current \( i \) is marked on the left branch flowing counterclockwise.
   - The voltage \( V_x \) is marked across the middle 5Ω resistor with positive on the left and negative on the right.

**Objective:**

Calculate the marked current \( i \) and the voltage \( V_x \) using circuit analysis techniques such as mesh or nodal analysis.
Transcribed Image Text:**Problem:** Find the marked current \( i \) and voltage \( V_x \) in the following circuit diagram. **Diagram Description:** The circuit consists of a network of resistors and a voltage source. Here’s a detailed breakdown of the circuit: 1. **Voltage Source:** - A 10V voltage source is connected on the left side of the circuit. 2. **Resistors:** - Multiple resistors are connected in the circuit with the following resistances: - Two 5Ω resistors - Two 20Ω resistors - Six 10Ω resistors 3. **Connections:** - The top path from left to right includes two consecutive 10Ω resistors. - Below the top path, in a triangular configuration, there is a 5Ω resistor in series from the + terminal of the voltage source leading to a 20Ω resistor, followed by another 5Ω resistor. - The middle horizontal line consists of two 10Ω resistors. - Below this line, another set of configurations includes a 5Ω, a 10Ω, and another set with 20Ω connected vertically on the right side. - Bottom line includes two 10Ω resistors. 4. **Current and Voltage Markings:** - The current \( i \) is marked on the left branch flowing counterclockwise. - The voltage \( V_x \) is marked across the middle 5Ω resistor with positive on the left and negative on the right. **Objective:** Calculate the marked current \( i \) and the voltage \( V_x \) using circuit analysis techniques such as mesh or nodal analysis.
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