To solve the problem depicted in the circuit diagram, we need to calculate the voltage that will be displayed on the voltmeter when the ammeter reads 0.6 A.

Step-by-Step Analysis:

1. Understanding the Circuit:

   • The circuit consists of three resistors:
     • A $3 \, \Omega$ resistor in series with the ammeter (A),
     • A parallel combination of $4 \, \Omega$ and $8 \, \Omega$ resistors.
   • The voltmeter (V) measures the voltage across the parallel combination of the $4 \, \Omega$ and $8 \, \Omega$ resistors.

2. Total Current and Voltage: The ammeter indicates that the current in the series part of the circuit is $0.6 \, A$. This current flows through the $3 \, \Omega$ resistor and then splits between the two branches with the $4 \, \Omega$ and $8 \, \Omega$ resistors.

3. Step 1: Calculating the Equivalent Resistance of the Parallel Resistors The formula for the equivalent resistance $R_{eq}$ of two resistors in parallel is:

   $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$ where $R_1 = 4 \, \Omega$ and $R_2 = 8 \, \Omega$.

   $\frac{1}{R_{eq}} = \frac{1}{4} + \frac{1}{8} = \frac{2 + 1}{8} = \frac{3}{8}$

   So, the equivalent resistance $R_{eq}$ of the parallel resistors is:

   $R_{eq} = \frac{8}{3} \, \Omega \approx 2.67 \, \Omega$

4. Step 2: Calculating Total Resistance of the Circuit The total resistance $R_{total}$ is the sum of the $3 \, \Omega$ resistor and the equivalent resistance of the parallel combination:

   $R_{total} = 3 \, \Omega + 2.67 \, \Omega = 5.67 \, \Omega$

5. Step 3: Finding the Voltage of the Battery (E) Using Ohm's law $V = I \times R$, the voltage $E$ across the whole circuit can be calculated:

   $E = I \times R_{total} = 0.6 \, A \times 5.67 \, \Omega = 3.4 \, V$

6. Step 4: Voltage Across the Parallel Combination Since the $3 \, \Omega$ resistor is in series, the voltage across this resistor is:

   $V_{3 \, \Omega} = I \times R = 0.6 \, A \times 3 \, \Omega = 1.8 \, V$

   The voltage measured by the voltmeter is the remaining voltage across the parallel branch:

   $V_{parallel} = E - V_{3 \, \Omega} = 3.4 \, V - 1.8 \, V = 1.6 \, V$

Answer:

The value measured by the voltmeter is 1.6 V.

Would you like further clarifications or details on any part of this explanation?

Here are 5 questions to extend your understanding:

1. How do you calculate the current through each branch in a parallel circuit?
2. What would happen if the resistance values in the parallel branch were different?
3. How does the total resistance change if another resistor is added in parallel?
4. Can you explain how the voltmeter works in a parallel circuit?
5. What would the total voltage be if the current increased to 1 A?

Tip: Always verify the configuration of the resistors (series or parallel) when solving circuit problems; it affects how you sum up resistances.