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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

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A voltmeter has a resistance of 4.0 kΩ and reads 1.0 V for every scale division on the meter. A power supply of emf 20 V and negligible internal resistance is conne... show full transcript

Worked Solution & Example Answer: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

Step 1

Calculate the Total Voltage Drop

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Answer

The voltmeter reads 2 divisions, corresponding to a voltage drop of: Vm=2imes1.0extV=2.0extVV_m = 2 imes 1.0 ext{ V} = 2.0 ext{ V}

Step 2

Determine the Currents and Resistance

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Given the total emf of the circuit is 20 V, the voltage across the resistor is: VR=E−Vm=20extV−2.0extV=18.0extVV_R = E - V_m = 20 ext{ V} - 2.0 ext{ V} = 18.0 ext{ V}

Using Ohm's law, we can find the total current in the series: I=VmRm=2.0extV4.0extkΩ=0.0005extAI = \frac{V_m}{R_m} = \frac{2.0 ext{ V}}{4.0 ext{ kΩ}} = 0.0005 ext{ A}

Step 3

Calculate the Resistor Value

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Now, using Ohm's law again for the resistor: R=VRI=18.0extV0.0005extA=36extkΩR = \frac{V_R}{I} = \frac{18.0 ext{ V}}{0.0005 ext{ A}} = 36 ext{ kΩ}

Thus, the value of the resistor is 36 kΩ.

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