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The battery had a power output of 230 mW when the resistance of the variable resistor was 36 Ω - AQA - GCSE Physics - Question 7 - 2021 - Paper 1

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The battery had a power output of 230 mW when the resistance of the variable resistor was 36 Ω. Determine the potential difference across the battery. Potential di... show full transcript

Worked Solution & Example Answer:The battery had a power output of 230 mW when the resistance of the variable resistor was 36 Ω - AQA - GCSE Physics - Question 7 - 2021 - Paper 1

Step 1

Determine the Current from Power

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Answer

To find the current, we use the formula for power:

P=IVP = IV

Where:

  • P=230 mW=0.230 WP = 230 \text{ mW} = 0.230 \text{ W},
  • II is the current in amps,
  • VV is the potential difference.

Rearranging for current gives: I=PVI = \frac{P}{V}

Using the resistance value of 36 Ω, we can express the potential difference as: V=I×RV = I \times R Substituting the current back into the equation gives: V=0.230 W×1IV = 0.230 \text{ W} \times \frac{1}{I}

Step 2

Calculate the Potential Difference

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Answer

Substituting the current from Ohm's law:

V=I×36 ΩV = I \times 36\text{ Ω}

We previously found that: I=0.08 AI = 0.08\text{ A}

Therefore, V=0.08 A×36 Ω=2.88extVV = 0.08 \text{ A} \times 36\text{ Ω} = 2.88 ext{ V}

Thus, the potential difference across the battery is approximately 2.88 V.

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