A voltmeter has a resistance of 4.0 kΩ and reads 1.0 V for every scale division on the meter - AQA - A-Level Physics - Question 24 - 2019 - Paper 1

To find the value of the resistor, we start by analyzing the voltmeter's reading and the given circuit attributes.

1. Understanding the Circuit: The voltmeter (V_m) reads two divisions, which at 1 V per division means that $V_m = 2 ext{ V}$. The total voltage from the power supply (V) is 20 V. Thus, we have the voltage across the resistor (R) as: $V_R = V - V_m = 20 ext{ V} - 2 ext{ V} = 18 ext{ V}$

2. Using Ohm's Law: The voltage across the resistor can also be expressed using Ohm's Law as: $V_R = I imes R$ where $I$ is the current flowing through the circuit.

3. Calculating the Current: The current through the voltmeter can be calculated since:

   • The total resistance in series is $R + 4.0 ext{ kΩ}$.
   • The current $I$ is then: I = rac{V}{R + 4.0kΩ}

4. Setting up the Equation: Since we have: $18 ext{ V} = I imes R$ and substituting for I gives: 18 = rac{20}{R + 4.0} imes R

5. Rearranging the Formula: To solve for R, we can rearrange the equation to: $18(R + 4.0) = 20R$ which simplifies to: $18R + 72 = 20R$ thus, $2R = 72$ leading to: $R = 36 ext{ kΩ}$

6. Conclusion: Therefore, the value of the resistor is 36 kΩ, corresponding to option B.