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6 (a) A man monitors how much money he spends on electricity - Edexcel - GCSE Physics - Question 6 - 2015 - Paper 1

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6 (a) A man monitors how much money he spends on electricity. He uses a device which calculates the cost of electrical energy used. He connects his 2.9 kW electric... show full transcript

Worked Solution & Example Answer:6 (a) A man monitors how much money he spends on electricity - Edexcel - GCSE Physics - Question 6 - 2015 - Paper 1

Step 1

Calculate the current in the kettle element.

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Answer

To find the current flowing through the kettle element, we can use Ohm's Law, which states:

P=IVP = IV

Where:

  • P is the power in watts (W)
  • I is the current in amperes (A)
  • V is the voltage in volts (V)

Given:

  • Power, P=2.9extkW=2900extWP = 2.9 ext{ kW} = 2900 ext{ W}
  • Voltage, V=230extVV = 230 ext{ V}

Rearranging Ohm's law to find current:

I=PVI = \frac{P}{V}

Substituting the given values:

I=2900230≈12.61extAI = \frac{2900}{230} \approx 12.61 ext{ A}

Therefore, the current in the kettle element is approximately 12.61 A.

Step 2

Calculate the length of time for which the kettle has been switched on during the week.

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Answer

To calculate the length of time the kettle has been switched on, we first need to determine how much electrical energy the kettle has used during the week.

The cost of energy used is 97 pence, and the cost per kWh is 17 pence. Thus, we can calculate the total energy consumed in kWh:

extEnergy(kWh)=97extp17extp/kWh≈5.71extkWh ext{Energy (kWh)} = \frac{97 ext{ p}}{17 ext{ p/kWh}} \approx 5.71 ext{ kWh}

Next, we relate the energy used back to the power rating of the kettle to calculate the time:

extEnergy=extPower×extTime ext{Energy} = ext{Power} \times ext{Time}

Rearranging gives us:

extTime=extEnergyextPower ext{Time} = \frac{ ext{Energy}}{ ext{Power}}

Substituting the values:

extTime=5.71extkWh2.9extkW≈1.97exthours ext{Time} = \frac{5.71 ext{ kWh}}{2.9 ext{ kW}} \approx 1.97 ext{ hours}

Thus, the kettle has been switched on for approximately 1.97 hours during the week.

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