What is the reading of voltmeter in the following figure?

Resistance between A and B $=\frac{1000\times 500}{\left(1500\right)}=\frac{1000}{3}$

To solve this question, we need to determine what is the reading of the voltmeter in the following figure. Let us analyze the circuit step by step using the given values.

Step 1: Analyze the circuit

• The battery provides a voltage of 10 V.
• There are two resistors of 500 Ω each connected in series.
• A voltmeter of 1000 Ω resistance is connected across one of the resistors.

Step 2: Total resistance of the circuit

The total resistance in the circuit includes:

1. The two 500 Ω resistors in series.
2. The voltmeter, which is connected in parallel with one of the 500 Ω resistors.

Resistance in parallel

The 500 Ω resistor is in parallel with the voltmeter of 1000 Ω. The equivalent resistance (R_parallel) is calculated using the formula for parallel resistances:

1 / R_parallel = 1 / 500 + 1 / 1000

1 / R_parallel = 2 / 1000 + 1 / 1000 = 3 / 1000

R_parallel = 1000 / 3 ≈ 333.33 Ω

Total resistance

The second 500 Ω resistor is in series with the equivalent resistance of 333.33 Ω. The total resistance (R_total) is:

R_total = 500 + 333.33 = 833.33 Ω

Step 3: Total current in the circuit

The total current (I) in the circuit is given by Ohm's Law:

I = Voltage / Total Resistance = 10 / 833.33 ≈ 0.012 A (12 mA)

Step 4: Voltage drop across the parallel combination

The voltage drop (V_parallel) across the parallel combination of the voltmeter and the 500 Ω resistor is:

V_parallel = I × R_parallel = 0.012 × 333.33 ≈ 4 V

Step 5: Reading of the voltmeter

The voltmeter measures the voltage across the 500 Ω resistor it is connected to. Since the voltmeter is connected in parallel with the resistor, it will measure the same voltage as the parallel combination.

Thus, what is the reading of the voltmeter in the following figure? The answer is:

4 V

Final Answer:

d. 4 V

This step-by-step explanation shows how to calculate what is the reading of the voltmeter in the following figure, ensuring simplicity and clarity for easy understanding.

$\mathrm{AB}=\frac{3}{250}\times \frac{1000}{3}=4\mathrm{V}$