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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
Question 24
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
What is the value of the resistor?
Answer
To find the value of the resistor, we start by analyzing the voltmeter's reading and the given circuit attributes.
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Understanding the Circuit: The voltmeter (V_m) reads two divisions, which at 1 V per division means that . The total voltage from the power supply (V) is 20 V. Thus, we have the voltage across the resistor (R) as:
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Using Ohm's Law: The voltage across the resistor can also be expressed using Ohm's Law as: where is the current flowing through the circuit.
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Calculating the Current: The current through the voltmeter can be calculated since:
- The total resistance in series is .
- The current is then: I = rac{V}{R + 4.0kΩ}
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Setting up the Equation: Since we have: and substituting for I gives: 18 = rac{20}{R + 4.0} imes R
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Rearranging the Formula: To solve for R, we can rearrange the equation to: which simplifies to: thus, leading to:
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Conclusion: Therefore, the value of the resistor is 36 kΩ, corresponding to option B.