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For the circuit in the figure below, the voltage Vac can be obtained as

To find the voltage \( V_{ac} \) across points \( a \) and \( c \), we need to calculate the total voltage drop across all the resistors in the circuit.

1. **Analyze the Circuit:** The circuit is a series circuit with resistors \( R_1 = 470 \, \Omega \), \( R_2 = 180 \, \Omega \), and \( R_3 = 390 \, \Omega \) in series with a \( 24 \, V \) voltage source.

2. **Total Resistance \( R_{total} \):**
   Since the resistors are in series, the total resistance is the sum of the resistances:
   \[
   R_{total} = R_1 + R_2 + R_3 = 470 \, \Omega + 180 \, \Omega + 390 \, \Omega = 1040 \, \Omega
   \]

3. **Calculate the Current \( I \):**
   Using Ohm's law \( V = IR \), the current \( I \) through the circuit is:
   \[
   I = \frac{V}{R_{total}} = \frac{24 \, V}{1040 \, \Omega} \approx 0.0231 \, A
   \]

4. **Voltage Across \( R_1 \), \( R_2 \), and \( R_3 \):**
   - Voltage across \( R_1 \):
     \[
     V_{R1} = I \cdot R_1 = 0.0231 \, A \cdot 470 \, \Omega \approx 10.857 \, V
     \]
   - Voltage across \( R_2 \):
     \[
     V_{R2} = I \cdot R_2 = 0.0231 \, A \cdot 180 \, \Omega \approx 4.158 \, V
     \]
   - Voltage across \( R_3 \):
     \[
     V_{R3} = I \cdot R_3 = 0.0231 \, A \cdot 390 \, \Omega \approx 9.009 \, V
     \]

5. **Voltage \( V_{ac} \):**
   Since the total voltage is the sum of the voltage drops across \( R_1 \), \( R_2 \), and \( R_3 \), we find that:
   \[
   V_{ac} = V_{R1} + V_{R2} + V_{R3} = 10.857 \, V + 4.158 \, V + 9.009 \, V = 24 \, V
   \]

Therefore, the voltage \( V_{ac} \) is indeed **24 V**, as it is the total voltage supplied by the source.

Would you like more details or have any questions?

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### Related Questions:

1. What would happen to \( V_{ac} \) if \( R_2 \) were doubled?
2. How would the total current change if \( R_3 \) were removed?
3. Can we calculate the power dissipated by each resistor?
4. What effect would increasing the supply voltage have on \( V_{ac} \)?
5. How would the current change if an additional resistor were added in series?

### Tip:
In a series circuit, the current is constant across all elements, and the total voltage is the sum of individual voltage drops across each resistor.

For the circuit in the figure below, the voltage Vac can be obtained as

Explore how to find the voltage Vac across a series circuit with resistors R1 = 470Ω, R2 = 180Ω, and R3 = 390Ω connected to a 24V source. This solution covers Ohm's Law and series circuit calculations, suitable for students in Grades 10-12.

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