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To solve this problem using nodal analysis, we need to determine the voltages \( V_a \), \( V_b \), \( V_c \), and \( V_d \) at each node. Here’s a step-by-step approach:

### Step 1: Assign Node Voltages
- Assume ground (0V) is at the bottom node where the current source is connected.
- Label each node as follows:
  - \( V_a \): Node voltage across the 5 Ω resistor on the far right.
  - \( V_b \): Node voltage across the 10 Ω resistor on the far left.
  - \( V_c \): Node voltage between the 20 Ω and 5 Ω resistors.
  - \( V_d \): Node voltage between the 10 Ω resistor on the right and the 10 Ω resistor on the left of it.

### Step 2: Set Up Node Equations Using Kirchhoff’s Current Law (KCL)
For each node, the sum of currents leaving the node should equal zero.

#### Node at \( V_c \):
The currents leaving the node are:
- Through the 20 Ω resistor: \(\frac{V_c - V_d}{20}\)
- Through the 5 Ω resistor to \( V_b \): \(\frac{V_c - V_b}{5}\)
- Through the 10 Ω resistor to \( V_a \): \(\frac{V_c - V_a}{10}\)

The KCL equation at \( V_c \) is:
\[
\frac{V_c - V_d}{20} + \frac{V_c - V_b}{5} + \frac{V_c - V_a}{10} = 0
\]

#### Node at \( V_d \):
The currents leaving the node are:
- Through the 10 Ω resistor to \( V_a \): \(\frac{V_d - V_a}{10}\)
- Through the 20 Ω resistor to \( V_c \): \(\frac{V_d - V_c}{20}\)

The KCL equation at \( V_d \) is:
\[
\frac{V_d - V_a}{10} + \frac{V_d - V_c}{20} = 0
\]

#### Node at \( V_b \):
The current entering the node from the 10 Ω resistor is balanced by the current leaving the 5 Ω resistor to \( V_c \).

The KCL equation at \( V_b \) is:
\[
\frac{V_b - V_c}{5} = \frac{V_b}{10}
\]

#### Node at \( V_a \):
The current entering the node from the 5 Ω resistor is balanced by the current leaving through the 10 Ω resistor to \( V_d \).

The KCL equation at \( V_a \) is:
\[
\frac{V_a - V_c}{10} = \frac{V_a}{5}
\]

### Step 3: Substitute Known Values and Solve the Equations
Using the above equations, we can solve for the voltages \( V_a \), \( V_b \), \( V_c \), and \( V_d \) by substituting into each equation and solving the resulting system.

Would you like me to continue with detailed calculations or provide a solution based on these setups?

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Here are five related questions to expand understanding:
1. How does nodal analysis differ from mesh analysis?
2. What role does Kirchhoff’s Current Law play in nodal analysis?
3. How would the solution change if there were a voltage source instead of a current source?
4. Can we apply nodal analysis directly if there’s a dependent current source?
5. What steps should we take if we want to find the power dissipated in each resistor?

**Tip:** For complex circuits, organizing your nodes and labeling currents clearly can simplify nodal analysis calculations.

Use nodal analysis to find voltages Va, Vb, Vc, and Vd in the given circuit.

Learn how to use nodal analysis to calculate voltages Va, Vb, Vc, and Vd in a circuit featuring resistors of 5Ω, 10Ω, and 20Ω, along with a 10A current source. This solution covers core concepts of nodal analysis, Kirchhoff's Current Law (KCL), and Ohm's Law, ideal for electrical engineering students.

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