https://file.aiquickdraw.com/mathbot/file/1725899319908trnr4kgd.jpg

To find the voltage \( V_A \) in the given circuit, we can apply Kirchhoff's Voltage Law (KVL). KVL states that the sum of all voltages around a closed loop in a circuit must equal zero.

### Step 1: Analyze the Circuit

The circuit consists of two loops with two voltage sources:
- A 17V source on the left
- A 10V source on the right

Resistances:
- 2Ω and 5Ω in the left loop
- 1Ω and 5Ω in the right loop

The voltage \( V_A \) is across the 5Ω resistor.

### Step 2: Write the KVL Equations

For the left loop (starting from the 17V source):
\[
17V - 2I_1 - 5I_3 = 0 \quad \text{(1)}
\]
Where \( I_1 \) is the current through the 2Ω resistor, and \( I_3 \) is the current through the 5Ω resistor.

For the right loop (starting from the 10V source):
\[
10V - 1I_2 - 5I_3 = 0 \quad \text{(2)}
\]
Where \( I_2 \) is the current through the 1Ω resistor, and \( I_3 \) is the current through the 5Ω resistor (same \( I_3 \) as in equation (1)).

### Step 3: Solve for Currents

Using the equations above, we can solve for the currents and then find \( V_A = I_3 \times 5Ω \).

Let me calculate this for you.It seems there was an issue with solving the system of equations. I will try an alternative method to correctly find the currents and the voltage \( V_A \). 

Let me retry the calculation.The voltage \( V_A \) across the 5Ω resistor is calculated to be 5V. However, the answer choices in the question are higher, so we need to revisit our equations.

Let's recheck the steps, adjusting for any earlier assumptions, and solve for the correct values.After carefully revisiting the calculations, the voltage across the 5Ω resistor \( V_A \) still results in 5V. However, this does not align with the provided answer choices.

This discrepancy might indicate the need to consider the given resistances and voltage sources more closely, or a simplification of assumptions. If you're solving similar problems, I would recommend carefully verifying the resistor arrangements and loop directions.

### Tip:
Always double-check the current directions and apply Kirchhoff's laws accurately in multi-loop circuits to avoid calculation errors.

For the circuit shown in the figure above, what is the voltage VA?

Learn how to calculate the voltage VA in a circuit with multiple loops using Kirchhoff's Voltage Law (KVL) and Ohm's Law. This example involves solving a system of linear equations derived from KVL. Suitable for undergraduate students studying electrical engineering.

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