Question

The reading of the voltmeter is :

• A. 4 V
• B. 3 V
• C. 8 V
• D. 6 V

Hint:

To find the voltage across a specific resistor in a series circuit, first find the total current flowing through the circuit, then apply Ohm's law ($V=IR$) to that specific resistor.

Answer 1

The Correct Option is C

Step 1: Identify the components and configuration in the circuit.
The circuit has a 12V battery. There's a $4 \, \Omega$ resistor in series with a parallel combination of a $3 \, \Omega$ resistor and a $6 \, \Omega$ resistor. The voltmeter is connected across the $4 \, \Omega$ resistor. We need to find the voltage across the $4 \, \Omega$ resistor. Step 2: Calculate the equivalent resistance of the parallel combination.
For two resistors in parallel, the equivalent resistance ($R_{eq,parallel}$) is given by:
$\frac{1}{R_{eq,parallel}} = \frac{1}{R_1} + \frac{1}{R_2}$
Here, $R_1 = 3 \, \Omega$ and $R_2 = 6 \, \Omega$.
$\frac{1}{R_{eq,parallel}} = \frac{1}{3} + \frac{1}{6} = \frac{2 + 1}{6} = \frac{3}{6} = \frac{1}{2}$
$R_{eq,parallel} = 2 \, \Omega$
Step 3: Calculate the total equivalent resistance of the circuit.
The $4 \, \Omega$ resistor is in series with the parallel combination ($2 \, \Omega$).
For resistors in series, the total equivalent resistance ($R_{total}$) is the sum of individual resistances:
$R_{total} = R_{series} + R_{eq,parallel}$
$R_{total} = 4 \, \Omega + 2 \, \Omega = 6 \, \Omega$
Step 4: Calculate the total current flowing through the circuit.
Using Ohm's Law, $V = IR$, where $V$ is the total voltage, $I$ is the total current, and $R$ is the total equivalent resistance.
$I_{total} = \frac{V_{total}}{R_{total}}$
Given $V_{total} = 12 \, \text{V}$ and $R_{total} = 6 \, \Omega$.\ $I_{total} = \frac{12 \, \text{V}}{6 \, \Omega} = 2 \, \text{A}$
Step 5: Calculate the voltage across the $4 \, \Omega$ resistor.
Since the $4 \, \Omega$ resistor is in the main series path, the total current ($I_{total} = 2 \, \text{A}$) flows through it. Using Ohm's Law for the $4 \, \Omega$ resistor: $V_{4\Omega} = I_{total} \times R_{4\Omega}$ $V_{4\Omega} = 2 \, \text{A} \times 4 \, \Omega = 8 \, \text{V}$ Step 6: Conclude the reading of the voltmeter.
The voltmeter is connected across the $4 \, \Omega$ resistor, so its reading will be 8 V. (3) 8 V