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Calculate the value of Vx in the following circuit, when the value for the sources and resistors are the following:

V1= 33 Volts

V2= 6.3 Volts

R1= 679 Ohms

R2= 566 Ohms

R3= 688 Ohms

R4= 135 Ohms

To calculate \( V_x \) in this circuit, we can use Kirchhoff's Voltage Law (KVL), which states that the sum of the voltages around any closed loop in a circuit must equal zero.

The circuit has two voltage sources (\( V_1 \) and \( V_2 \)) and four resistors (\( R_1 \), \( R_2 \), \( R_3 \), and \( R_4 \)) arranged in series.

### Steps to Solve:
1. **Determine the total resistance** in the circuit:
   Since all resistors are in series, the total resistance \( R_{total} \) is the sum of all resistors:
   \[
   R_{total} = R_1 + R_2 + R_3 + R_4
   \]

2. **Calculate the total voltage** \( V_{total} \):
   Using KVL, the total voltage in the circuit, \( V_{total} \), is the sum of \( V_1 \) and \( V_2 \):
   \[
   V_{total} = V_1 - V_2
   \]

3. **Calculate the total current** \( I \):
   Ohm's Law states \( I = \frac{V_{total}}{R_{total}} \).

4. **Calculate \( V_x \)**:
   The voltage across \( R_4 \) (labeled \( V_x \)) can be found using Ohm's Law:
   \[
   V_x = I \times R_4
   \]

### Substituting Values:

- \( V_1 = 33 \, \text{V} \)
- \( V_2 = 6.3 \, \text{V} \)
- \( R_1 = 679 \, \Omega \)
- \( R_2 = 566 \, \Omega \)
- \( R_3 = 688 \, \Omega \)
- \( R_4 = 135 \, \Omega \)

#### Step 1: Calculate \( R_{total} \)
\[
R_{total} = 679 + 566 + 688 + 135 = 2068 \, \Omega
\]

#### Step 2: Calculate \( V_{total} \)
\[
V_{total} = V_1 - V_2 = 33 - 6.3 = 26.7 \, \text{V}
\]

#### Step 3: Calculate \( I \)
\[
I = \frac{V_{total}}{R_{total}} = \frac{26.7}{2068} \approx 0.0129 \, \text{A} \, (\text{or } 12.9 \, \text{mA})
\]

#### Step 4: Calculate \( V_x \)
\[
V_x = I \times R_4 = 0.0129 \times 135 \approx 1.74 \, \text{V}
\]

### Answer:
The value of \( V_x \) is approximately \( 1.74 \, \text{V} \).

Would you like further details on any part of this solution?

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#### Related Questions:
1. How would the value of \( V_x \) change if \( R_4 \) were doubled?
2. What would happen to the total current if \( V_2 \) were increased?
3. How would adding another resistor in series affect \( V_x \)?
4. How could you measure \( V_x \) in a practical circuit setup?
5. What if the resistors were in parallel—how would the approach differ?

#### Tip:
Remember, in a series circuit, the current remains the same across each component, making it straightforward to calculate voltage drops across individual resistors.

Calculate the value of Vx in the following circuit, when the value for the sources and resistors are the following: V1= 33 Volts, V2= 6.3 Volts, R1= 679 Ohms, R2= 566 Ohms, R3= 688 Ohms, R4= 135 Ohms.

Learn how to calculate the voltage Vx in a series circuit with two voltage sources (33V and 6.3V) and four resistors. This problem covers Kirchhoff's Voltage Law, Ohm's Law, and total resistance in a series circuit. Suitable for high school students in Grades 9-12.

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