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A defibrillator is a device that provides a high energy electrical impulse to correct abnormal heart beats - Scottish Highers Physics - Question 11 - 2015

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A defibrillator is a device that provides a high energy electrical impulse to correct abnormal heart beats. The diagram shows a simplified version of a defibrillato... show full transcript

Worked Solution & Example Answer:A defibrillator is a device that provides a high energy electrical impulse to correct abnormal heart beats - Scottish Highers Physics - Question 11 - 2015

Step 1

Show the charge on the capacitor when it is fully charged is 0.16 C.

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Answer

To find the charge on the capacitor, we use the formula:

Q=CimesVQ = C imes V

where:

  • QQ is the charge,
  • CC is the capacitance (64 µF = 64imes106F64 imes 10^{-6} F),
  • VV is the voltage (2.50 kV = 2.50imes103V2.50 imes 10^{3} V).

Substituting the values, we get:

Q=64imes106Fimes2.50imes103VQ = 64 imes 10^{-6} F imes 2.50 imes 10^{3} V

Calculating this gives:

Q=0.16CQ = 0.16 C

Step 2

Calculate the maximum energy stored by the capacitor.

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Answer

The maximum energy stored in the capacitor is given by:

E=12CV2E = \frac{1}{2} C V^2

Substituting the given values:

E=12×(64×106F)×(2.50×103V)2E = \frac{1}{2} \times (64 \times 10^{-6} F) \times (2.50 \times 10^{3} V)^2

Calculating this yields:

E=200JE = 200 J

Step 3

Calculate the effective resistance of the part of the person’s body between the paddles.

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Answer

Using Ohm's Law, we can derive the resistance:
V=IimesRV = I imes R
Rearranging gives:
R=VIR = \frac{V}{I}
Where V is the voltage across the paddles (2.50 kV = 2.50imes103V2.50 imes 10^{3} V) and I is the initial discharge current (35 A):
R=2.50×103V35A71.43ΩR = \frac{2.50 \times 10^{3} V}{35 A} \approx 71.43 \Omega

Step 4

Explain why the current decreases with time.

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Answer

The current decreases with time due to the discharging of the capacitor. As the charge on the capacitor decreases while discharging through the person's body, the potential difference across the paddles also reduces, leading to a decrease in the current. Hence, even though the resistance remains constant, the current reduces because of the diminishing voltage.

Step 5

Add a line to show how the current in this case would appear.

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Answer

The new line on the graph will start at a lower initial current than the first case due to the larger effective resistance of the person. This will result in a slower decrease towards zero. The curve is expected to decline more gradually compared to the original person owing to higher resistance.

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