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?

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.